546 + Mcqs in Permutation and Combination Page 6 McqOptions

251.	In how many different ways can a person get his two guests stayed in 9 rooms when only one guest stays in one room?
A.	72
B.	6
C.	36
D.	81
Answer» D. 81

Discussion

252.	How many different six letter words can be formed using the letters of the word ‘PENCIL’ if repetition is not allowed?
A.	700
B.	720
C.	740
D.	760
Answer» C. 740

Discussion

253.	On simplification the product\((x_1 + y_1)(x_2 + y_2)...(x_{10} + y_{10})\)how many such terms are there which will have only single x and rest y's?
A.	\(2^{10}\)
B.	10
C.	20
D.	1
Answer» C. 20

Discussion

254.	How many different sums can be formed with the denominations Rs. 50, Rs. 100, Rs. 200, Rs. 500 and Rs. 2,000 taking at least three denominations at a time?
A.	16
B.	15
C.	14
D.	10
Answer» B. 15

Discussion

255.	How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
A.	5
B.	10
C.	15
D.	20
Answer» E.

Discussion

256.	In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
A.	32
B.	48
C.	36
D.	60
Answer» D. 60

Discussion

257.	A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
A.	32
B.	48
C.	64
D.	96
Answer» D. 96

Discussion

258.	In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
A.	10080
B.	4989600
C.	120960
D.	None of these
Answer» D. None of these

Discussion

259.	How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
A.	40
B.	400
C.	5040
D.	2520
Answer» D. 2520

Discussion

260.	How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?
A.	720
B.	24
C.	None of these
D.	120
Answer» E.

Discussion

261.	How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
A.	20
B.	16
C.	8
D.	24
Answer» B. 16

Discussion

262.	How many arrangements can be made out of the letters of the word 'ENGINEERING' ?
A.	924000
B.	277200
C.	None of these
D.	182000
Answer» C. None of these

Discussion

263.	How many words can be formed by using all letters of the word 'BIHAR'?
A.	720
B.	24
C.	120
D.	60
Answer» D. 60

Discussion

264.	In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
A.	None of these
B.	720
C.	420
D.	122
Answer» C. 420

Discussion

265.	How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
A.	720
B.	420
C.	None of these
D.	5040
Answer» B. 420

Discussion

266.	There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?
A.	10420
B.	11
C.	11760
D.	None of these
Answer» D. None of these

Discussion

267.	In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
A.	9800
B.	100020
C.	120960
D.	140020
Answer» D. 140020

Discussion

268.	In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
A.	1
B.	126
C.	63
D.	64
Answer» D. 64

Discussion

269.	In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?
A.	None of these
B.	720
C.	60
D.	120
Answer» E.

Discussion

270.	Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
A.	120
B.	720
C.	125
D.	729
Answer» E.

Discussion

271.	In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
A.	2880
B.	1400
C.	1200
D.	3212
Answer» B. 1400

Discussion

272.	A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?
A.	None of these
B.	6020
C.	1200
D.	9450
Answer» E.

Discussion

273.	A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours?
A.	62
B.	48
C.	12
D.	24
Answer» E.

Discussion

274.	25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
A.	None of these
B.	600
C.	12
D.	24
Answer» C. 12

Discussion

275.	An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?
A.	100
B.	80
C.	110
D.	64
Answer» C. 110

Discussion

276.	How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
A.	720
B.	360
C.	1420
D.	1680
Answer» E.

Discussion

277.	Find the number of diagonals formed in hexagon .
A.	12
B.	10
C.	6
D.	9
Answer» E.

Discussion

278.	There is a polygon of 12 sides . How many triangles can be drawn using the vertices of polygon ?
A.	200
B.	220
C.	240
D.	260
Answer» C. 240

Discussion

279.	In how many ways, a cricket team of 11 players can be made from 15 players, if a particulars player is always chosen ?
A.	1835
B.	1001
C.	1635
D.	1365
Answer» C. 1635

Discussion

280.	In how many ways, a committee of 3 men and 2 women can be formed out of a total of 4 men and 4 women ?
A.	15
B.	16
C.	20
D.	24
Answer» E.

Discussion

281.	How many necklaces of 12 beads can be made from 18 beads of various colours ?
A.	[118 x 13!] / 2
B.	[110 x 14! ] / 2
C.	[119 x 13!] / 2
D.	[110 x 12!] / 2
Answer» D. [110 x 12!] / 2

Discussion

282.	In how many different ways, 5 boys and 5 girls can sit on a circular table, so that the boys and girls are alternate ?
A.	2880
B.	2800
C.	2680
D.	2280
Answer» B. 2800

Discussion

283.	20 persons were invited to a party. In how many ways, they and the host can be seated at a circular table ?
A.	18 !
B.	19 !
C.	20 !
D.	Couldn't be determined
Answer» D. Couldn't be determined

Discussion

284.	Find the number of ways, in which 12 different beads can be arranged to form a necklace .
A.	11 !/2
B.	10 !/2
C.	12 !/2
D.	Couldn't be determined
Answer» B. 10 !/2

Discussion

285.	In how many ways, can the letters of the word 'ASSASSINATION' be arranged, so that all the S are together ?
A.	10!
B.	14! (4!)
C.	151200
D.	3628800
Answer» D. 3628800

Discussion

286.	A child has four pockets and three marbles. In how many ways, the child can put the marbles in the pockets ?
A.	12
B.	64
C.	256
D.	60
Answer» C. 256

Discussion

287.	Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they are to be filled with either a red or a blue ball such that no two adjacent boxes can be filled with blue balls Then, how different arrangeme
A.	8
B.	10
C.	15
D.	22
Answer» E.

Discussion

288.	In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position ?
A.	9
B.	12
C.	14
D.	18
Answer» C. 14

Discussion

289.	A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees ?
A.	320
B.	160
C.	80
D.	200
Answer» C. 80

Discussion

290.	A department had 8 male and female employees each. A project team involving 3 male and 3 female members needs to be chosen from the department employees. How many different projects teams can be chose
A.	112896
B.	3136
C.	720
D.	112
Answer» C. 720

Discussion

291.	Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women. ?
A.	30
B.	20
C.	10
D.	25
Answer» B. 20

Discussion

292.	Find the number of ways of preparing a chain with 5 different coloured beads ?
A.	18
B.	24
C.	12
D.	30
Answer» D. 30

Discussion

293.	If there are 12 persons in a party and each of them shakes hands with each other, how many handshakes do happen in the party?
A.	77
B.	66
C.	44
D.	55
Answer» C. 44

Discussion

294.	In a monthly test, the teacher decides that there will be there questions, one each from ex. 7, 8 and 9 of the text book. There are 12 questions in ex-7 , 18 in ex-8 and 9 in ex-9. In how many ways ca
A.	1944
B.	2094
C.	1894
D.	2194
Answer» B. 2094

Discussion

295.	139 person have signed for an elimination tournament. All players are to be paired up for the first round but because 139 is an odd number one player gets a bye, which promotes him to the second round
A.	136
B.	137
C.	138
D.	139
Answer» D. 139

Discussion

296.	2 Men and 1 women board a bus in which 5 seats are vacant, one of these 5 seats is reserved for ladies. A women may or may not sit on the seat reserved for ladies . In how many different ways can the
A.	15
B.	36
C.	48
D.	60
Answer» C. 48

Discussion

297.	Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat ?
A.	4!
B.	8!
C.	6!
D.	9!
Answer» C. 6!

Discussion

298.	How many different numbers can be formed from the digits 3, 4, 5, 6 and 7 when repetitions are allowed ?
A.	3125
B.	625
C.	3905
D.	125
Answer» D. 125

Discussion

299.	Three dice (each having six faces with each face having one number from 1 or 6 ) are rolled. What is the number of possible outcomes such that atleast one dice shows the numbers 2 ?
A.	36
B.	81
C.	91
D.	116
Answer» D. 116

Discussion

300.	A, B , C , and D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns, so that the roads do not form a triangle, is ?
A.	7
B.	8
C.	9
D.	24
Answer» E.

Discussion

Explore topic-wise MCQs in General Aptitude.

In how many different ways can a person get his two guests stayed in 9 rooms when only one guest stays in one room?

How many different six letter words can be formed using the letters of the word ‘PENCIL’ if repetition is not allowed?

On simplification the product\((x_1 + y_1)(x_2 + y_2)...(x_{10} + y_{10})\)how many such terms are there which will have only single x and rest y's?

How many different sums can be formed with the denominations Rs. 50, Rs. 100, Rs. 200, Rs. 500 and Rs. 2,000 taking at least three denominations at a time?

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

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

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

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?

How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?

How many arrangements can be made out of the letters of the word 'ENGINEERING' ?

How many words can be formed by using all letters of the word 'BIHAR'?

In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?

How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?

In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?

Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?

In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?

A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?

A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours?

25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?

An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?

How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?

Find the number of diagonals formed in hexagon .

There is a polygon of 12 sides . How many triangles can be drawn using the vertices of polygon ?

In how many ways, a cricket team of 11 players can be made from 15 players, if a particulars player is always chosen ?

In how many ways, a committee of 3 men and 2 women can be formed out of a total of 4 men and 4 women ?

How many necklaces of 12 beads can be made from 18 beads of various colours ?

In how many different ways, 5 boys and 5 girls can sit on a circular table, so that the boys and girls are alternate ?

20 persons were invited to a party. In how many ways, they and the host can be seated at a circular table ?

Find the number of ways, in which 12 different beads can be arranged to form a necklace .

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

A child has four pockets and three marbles. In how many ways, the child can put the marbles in the pockets ?

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they are to be filled with either a red or a blue ball such that no two adjacent boxes can be filled with blue balls Then, how different arrangeme

In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position ?

A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees ?

A department had 8 male and female employees each. A project team involving 3 male and 3 female members needs to be chosen from the department employees. How many different projects teams can be chose

Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women. ?

Find the number of ways of preparing a chain with 5 different coloured beads ?

If there are 12 persons in a party and each of them shakes hands with each other, how many handshakes do happen in the party?

In a monthly test, the teacher decides that there will be there questions, one each from ex. 7, 8 and 9 of the text book. There are 12 questions in ex-7 , 18 in ex-8 and 9 in ex-9. In how many ways ca

139 person have signed for an elimination tournament. All players are to be paired up for the first round but because 139 is an odd number one player gets a bye, which promotes him to the second round

2 Men and 1 women board a bus in which 5 seats are vacant, one of these 5 seats is reserved for ladies. A women may or may not sit on the seat reserved for ladies . In how many different ways can the

Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat ?

How many different numbers can be formed from the digits 3, 4, 5, 6 and 7 when repetitions are allowed ?

Three dice (each having six faces with each face having one number from 1 or 6 ) are rolled. What is the number of possible outcomes such that atleast one dice shows the numbers 2 ?

A, B , C , and D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns, so that the roads do not form a triangle, is ?