546 + Mcqs in Permutation and Combination in General Aptitude Page 5 McqOptions

201.	From a group of 7 men 6 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
A.	64
B.	45
C.	35
D.	56
E.	one of these
Answer» E. one of these

Discussion

202.	In how many different ways can the letters of the word ALLAHABAD be arranged?
A.	780
B.	890
C.	560
D.	520
E.	one of these
Answer» D. 520

Discussion

203.	In how many different ways can the letters of the word CREAM be arranged?
A.	5
B.	20
C.	60
D.	80
E.	one of these
Answer» C. 60

Discussion

204.	A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associate. In how many different ways can this be done if the committee should have 2 trainees and 3 research associates?
A.	5
B.	5
C.	0
D.
Answer» D.

Discussion

205.	In how many different ways can the letters of the word AWARE be arranged?
A.	8
B.	0
C.	20
D.	60
E.	one of these
Answer» C. 20

Discussion

206.	A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors?
A.	2
B.	3
C.	4
D.	2
E.	one of these
Answer» F.

Discussion

207.	In how many different ways can the letters of the word BANANA be arranged?
A.	0
B.	20
C.	60
D.	20
E.	one of these
Answer» B. 20

Discussion

208.	Out of 5 men and 3 women, a committee of three members is to be formed so that it has 1 women, and 2 men. In how many different ways can it be done?
A.	0
B.	0
C.	3
D.	0
E.	one of these
Answer» E. one of these

Discussion

209.	A box contains 2 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least 1 black ball is to be included in the draw?
A.	2
B.	8
C.	4
D.	6
E.	one of these
Answer» D. 6

Discussion

210.	In how many different ways can the letters of the word BANKING be arranged in such a way that the vowels always come together?
A.	20
B.	40
C.	60
D.	40
E.	20
Answer» F.

Discussion

211.	In how many different ways can the letters of the word CREATE be arranged?
A.	5
B.	6
C.	60
D.	20
E.	one of these
Answer» D. 20

Discussion

212.	In how many different ways can the letters of the word INCREASE be arranged?
A.	0320
B.	0080
C.	0160
D.	4
E.	one of these
Answer» D. 4

Discussion

213.	A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways the committee can be formed if it should have 2 men and 3 women?
A.	6
B.	6
C.	5
D.	0
E.	one of these
Answer» E. one of these

Discussion

214.	In how many different ways can the letters of the word CAPITAL be arranged so that the vowels always come together?
A.	20
B.	60
C.	20
D.	40
E.	one of these
Answer» C. 20

Discussion

215.	In how many different ways can the letters of the word ‘TRANSPIRATION’ be arranged so that the vowels always come together?
A.	429500
B.	360800
C.	627800
D.	one of these
Answer» C. 627800

Discussion

216.	In how many different ways can the letters of the word RUMOUR be arranged?
A.	0
B.	0
C.	80
D.	20
E.	one of these
Answer» D. 20

Discussion

217.	In how many different ways can the letters of the word GAMBLE be arranged?
A.	5
B.	5
C.	0
D.	25
E.	one of these
Answer» F.

Discussion

218.	In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
A.	66
B.	040
C.	1760
D.	6400
E.	one of these
Answer» D. 6400

Discussion

219.	Out of 5 women and 4 men, a committee of three members is to be formed in such a way that at least one member is a women. In how many different ways can it be done ?
A.	6
B.	0
C.	4
D.	6
E.	one of these
Answer» C. 4

Discussion

220.	In how many different ways can the letters of the word OPERATE be arranged ?
A.	60
B.	20
C.	040
D.	520
E.	one of these
Answer» E. one of these

Discussion

221.	a, b, c, d and e are five natural numbers. Find the number of ordered sets (a, b, c, d, e) possible such that a + b + c + d + e = 64.
A.	4C5
B.	3C4
C.	5C4
D.	3C5
Answer» C. 5C4

Discussion

222.	In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
A.	72000
B.	2600
C.	5920
D.	3200
Answer» E.

Discussion

223.	Findthetotalnumberofdistinctvehiclenumbersthatcanbeformedusingtwo letters followed by two numbers. Letters need to be distinct.
A.	0000
B.	5000
C.	0000
D.	5000
Answer» C. 0000

Discussion

224.	There are five women and six men in a group.From this group a committee of 4 is to be chosen.How many different ways can a committee be formed that contain three women and one man?
A.	5
B.	0
C.	5
D.	92
Answer» C. 5

Discussion

225.	In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
A.	4
B.	8
C.	6
D.	4
Answer» C. 6

Discussion

226.	12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.
A.	60
B.	84
C.	32
D.	70
Answer» C. 32

Discussion

227.	If $$5{ \times ^{\text{n}}}{{\text{P}}_3} = 4{ \times ^{\left( {{\text{n}} + 1} \right)}}{{\text{P}}_{3,}}$$find n?
A.	0
B.	1
C.	2
D.	4
Answer» E.

Discussion

228.	The number of positive integers which can be formed by using any number of digits from 0, 1, 2, 3, 4, 5 without repetition.
A.	200
B.	500
C.	600
D.	630
Answer» E.

Discussion

229.	A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
A.	05
B.	68
C.	20
D.	89
Answer» C. 20

Discussion

230.	How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?
A.	10
B.	05
C.	0P5
D.	0C5
Answer» B. 05

Discussion

231.	In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?
A.	9P7
B.	9C7
C.	8P7
D.	8C7
Answer» B. 9C7

Discussion

232.	A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr.X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?
A.	72
B.	72
C.	72
D.	72
Answer» C. 72

Discussion

233.	I have an amount of Rs. 10 lakh, which I went to invest in stocks of some companies. I always invest only amounts that are multiples of Rs 1 lakh in the stock of any company. If I can choose from among the stocks of five different companies, In how many ways can I invest the entire amount that I have?
A.	52
B.	50
C.	001
D.	089
Answer» D. 089

Discussion

234.	A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?
A.	914
B.	630
C.	724
D.	824
Answer» B. 630

Discussion

235.	A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.
A.	52
B.	40
C.	00
D.	40
Answer» B. 40

Discussion

236.	What is the value of 1 × 1! + 2 × 2! + 3 × 3! + . . . . . . . .n × n!where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1
A.	× (n - 1) × (n - 1)!
B.	n + 1)! - {n × (n - 1)}
C.	n + 1)! - n!
D.	n + 1)! - 1!
Answer» E.

Discussion

237.	If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
A.	4
B.	1
C.	2
D.	0
Answer» D. 0

Discussion

238.	A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:
A.	1530
B.	! × 360
C.	! × 480
D.	! × 240
Answer» D. ! × 240

Discussion

239.	How many different words can be formed using all the letters of the word ALLAHABAD?(a) When vowels occupy the even positions.(b)Both L do not occur together.
A.	560,60,1680
B.	890,120,650
C.	650,200,4444
D.	one of these
Answer» E.

Discussion

240.	A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is
A.	16
B.	15
C.	12
D.	8
Answer» C. 12

Discussion

241.	How many possible two-digit numbers can be formed by using the digits 3, 5 and 7 (repetition of digits is allowed)?
A.	10
B.	9
C.	7
D.	8
Answer» C. 7

Discussion

242.	A select a group of 4 members and is to be formed from 8 men and 6 women in such a way that the group must have at least 1 woman. In how many different ways can it be done?
A.	264
B.	728
C.	931
D.	1001
Answer» D. 1001

Discussion

243.	A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answer are possible ?
A.	20
B.	40
C.	512
D.	1024
Answer» E.

Discussion

244.	Each entry is the number of all possible matrices of 3 × 3 with 0 or 1, respectively.
A.	9
B.	18
C.	27
D.	512
Answer» E.

Discussion

245.	In how many ways can the letter of the word ASSASSINATION be arranged so that all the S are together?
A.	10!
B.	14!(4!)
C.	1,51,200
D.	36,28,800
Answer» D. 36,28,800

Discussion

246.	Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.The number of distinct seating arrangement possible is:
A.	8
B.	16
C.	4
D.	10
Answer» C. 4

Discussion

247.	In how many different ways can the letters of the word ‘DISPLAY’ be arranged?
A.	1430
B.	5040
C.	4840
D.	2410
Answer» C. 4840

Discussion

248.	In how many ways is it possible to choose 2 white squares and 1 black square on a chess board so that all the squares must not lie in the same row or column?
A.	12668
B.	6452
C.	9688
D.	28452
E.	15488
Answer» F.

Discussion

249.	Find the number of ways in which 2 players out of 6 players can be selected to form a term.
A.	16
B.	11
C.	15
D.	13
Answer» D. 13

Discussion

250.	How many ways a captain and a vice-captain can be selected from a team of 11 players?
A.	99
B.	110
C.	90
D.	22
Answer» C. 90

Discussion

Explore topic-wise MCQs in General Aptitude.

From a group of 7 men 6 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

In how many different ways can the letters of the word ALLAHABAD be arranged?

In how many different ways can the letters of the word CREAM be arranged?

A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associate. In how many different ways can this be done if the committee should have 2 trainees and 3 research associates?

In how many different ways can the letters of the word AWARE be arranged?

A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors?

In how many different ways can the letters of the word BANANA be arranged?

Out of 5 men and 3 women, a committee of three members is to be formed so that it has 1 women, and 2 men. In how many different ways can it be done?

A box contains 2 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least 1 black ball is to be included in the draw?

In how many different ways can the letters of the word BANKING be arranged in such a way that the vowels always come together?

In how many different ways can the letters of the word CREATE be arranged?

In how many different ways can the letters of the word INCREASE be arranged?

A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways the committee can be formed if it should have 2 men and 3 women?

In how many different ways can the letters of the word CAPITAL be arranged so that the vowels always come together?

In how many different ways can the letters of the word ‘TRANSPIRATION’ be arranged so that the vowels always come together?

In how many different ways can the letters of the word RUMOUR be arranged?

In how many different ways can the letters of the word GAMBLE be arranged?

In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?

Out of 5 women and 4 men, a committee of three members is to be formed in such a way that at least one member is a women. In how many different ways can it be done ?

In how many different ways can the letters of the word OPERATE be arranged ?

a, b, c, d and e are five natural numbers. Find the number of ordered sets (a, b, c, d, e) possible such that a + b + c + d + e = 64.

In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?

Findthetotalnumberofdistinctvehiclenumbersthatcanbeformedusingtwo letters followed by two numbers. Letters need to be distinct.

There are five women and six men in a group.From this group a committee of 4 is to be chosen.How many different ways can a committee be formed that contain three women and one man?

In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?

12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.

If $$5{ \times ^{\text{n}}}{{\text{P}}_3} = 4{ \times ^{\left( {{\text{n}} + 1} \right)}}{{\text{P}}_{3,}}$$find n?

The number of positive integers which can be formed by using any number of digits from 0, 1, 2, 3, 4, 5 without repetition.

A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?

How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?

In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?

A selection committee is to be chosen consisting of 5 ex-technicians. Now there are 12 representatives from four zones. It has further been decided that if Mr.X is selected, Y and Z will not be selected and vice-versa. In how many ways it can be done?

A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?

A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.

What is the value of 1 × 1! + 2 × 2! + 3 × 3! + . . . . . . . .n × n!where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1

If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

How many different words can be formed using all the letters of the word ALLAHABAD?(a) When vowels occupy the even positions.(b)Both L do not occur together.

A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is

How many possible two-digit numbers can be formed by using the digits 3, 5 and 7 (repetition of digits is allowed)?

A select a group of 4 members and is to be formed from 8 men and 6 women in such a way that the group must have at least 1 woman. In how many different ways can it be done?

A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answer are possible ?

Each entry is the number of all possible matrices of 3 × 3 with 0 or 1, respectively.

In how many ways can the letter of the word ASSASSINATION be arranged so that all the S are together?

Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.The number of distinct seating arrangement possible is:

In how many different ways can the letters of the word ‘DISPLAY’ be arranged?

In how many ways is it possible to choose 2 white squares and 1 black square on a chess board so that all the squares must not lie in the same row or column?

Find the number of ways in which 2 players out of 6 players can be selected to form a term.

How many ways a captain and a vice-captain can be selected from a team of 11 players?