258 + Mcqs in Permutations and Combinations Page 5 McqOptions

201.	From a deck of 52 cards, a 5 card hand is dealt.How may distinct five card hands are there if the queen of spades and the four of diamonds must be in the hand?
A.	52C5
B.	50C3
C.	52C4
D.	50C4
Answer» C. 52C4

Discussion

202.	From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?
A.	103336
B.	120000
C.	108336
D.	108333
Answer» D. 108333

Discussion

203.	From a bunch of flowers having 16 red roses and 14 white roses, four flowers have to be selected. In how many different ways can they be selected such that at least one red rose is selected?
A.	27405
B.	26584
C.	26585
D.	27404
Answer» E.

Discussion

204.	From 5 consonants and 4 vowels, how many words can be formed using 3Â consonants and 2 vowels ?
A.	7600
B.	7200
C.	6400
D.	3600
Answer» C. 6400

Discussion

205.	Four ladies A, B, C and D and four gentlemen E, F, G and H are sitting in a circle round a table facing each other._x005F_x000D_ Directions:_x005F_x000D_ (1) No two ladies or two gentlemen are sitting side by side._x005F_x000D_ (2) C, who is sitting between G and E is facing D._x005F_x000D_ (3) F is between D and A and is facing G._x005F_x000D_ (4) H is to the right of B._x005F_x000D_ Question:_x005F_x000D_ 1. Who are immediate neighbours of B?_x005F_x000D_ 2. E is facing whom?
A.	G & H , H
B.	F & H , B
C.	E & F , F
D.	E & H , G
Answer» B. F & H , B

Discussion

206.	First,second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered.In how many different ways can the prizes be awarded?
A.	1736
B.	1716
C.	1216
D.	1346
Answer» C. 1216

Discussion

207.	Find the value of 'n' for which the nth term of two AP'S:_x005F_x000D_ 15,12,9.... and -15,-13,-11...... are equal?
A.	n = 2
B.	n = 5
C.	n = 29/5
D.	n = 1
Answer» D. n = 1

Discussion

208.	Find the total numbers greater than 4000 that can be formed with digits 2, 3, 4, 5, 6 no digit being repeated in any number ?
A.	120
B.	256
C.	192
D.	244
Answer» D. 244

Discussion

209.	Find the total number of distinct vehicle numbers that can be formed using twoÂ letters followed by two numbers. Letters need to be distinct
A.	65000
B.	64000
C.	72000
D.	36000
Answer» B. 64000

Discussion

210.	Find the sum of the all the numbers formed by the digits 2,4,6 and 8 without repetition. Number may be of any of the form like 2,24,684,4862 ?
A.	133345
B.	147320
C.	13320
D.	145874
Answer» C. 13320

Discussion

211.	Find the number of ways to take 4 people and place them in groups of 3 at a time whereÂ order does not matter?
A.	4
B.	12
C.	36
D.	16
Answer» B. 12

Discussion

212.	Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.
A.	28
B.	14
C.	21
D.	7
Answer» B. 14

Discussion

213.	Find the number of ways to arrange 6 items in groups of 4 at a time where order matters?
A.	720
B.	640
C.	740
D.	360
Answer» E.

Discussion

214.	Find the number of ways to take 20 objects and arrange them in groups of 5 at a timeÂ where order does not matter.?
A.	57090
B.	15540
C.	15504
D.	23670
Answer» D. 23670

Discussion

215.	Find the number of ways to draw a straight, (suit does not matter) beginning with a 4 andÂ ending with a 8?
A.	1024
B.	1296
C.	1094
D.	1200
Answer» B. 1296

Discussion

216.	Find the number of ways to arrange 4 people in groups of 3 at a time where orderÂ matters?
A.	20
B.	16
C.	24
D.	36
Answer» D. 36

Discussion

217.	Find the number of subsets of the set {1,2,3,4,5,6,7,8,9,10,11} having 4Â elements.
A.	340
B.	370
C.	320
D.	330
Answer» E.

Discussion

218.	Eight first class and six second class petty officers are on the board of the 56 club. InÂ how many ways can the members elect, from the board, a president, a vice-president,Â a secretary, and a treasurer if the president and secretary must be first class petty officersÂ and the vice-president and treasurer must be second class petty officers?
A.	1500
B.	1860
C.	1680
D.	1640
Answer» D. 1640

Discussion

219.	Determine the total number of five-card hands that can be drawn from a deck of 52 cards.
A.	2589860
B.	2598970
C.	2598960
D.	2430803
Answer» D. 2430803

Discussion

220.	Consider the word ROTOR. Whichever way you read it, from left to right orÂ from right to left, you get the same word. Such a word is known as palindrome. Find theÂ maximum possible number of 5-letter palindromes.
A.	17756
B.	17576
C.	12657
D.	12666
Answer» C. 12657

Discussion

221.	Compute the sum of 4 digit numbers which can be formed with the four digits 1,3,5,7, if each digit is used only once in each arrangement.
A.	105555
B.	106665
C.	106656
D.	108333
Answer» D. 108333

Discussion

222.	A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
A.	126
B.	120
C.	146
D.	156
Answer» B. 120

Discussion

223.	A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls.How many councils can have Jason on the council?
A.	715
B.	725
C.	419
D.	341
Answer» B. 725

Discussion

224.	A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and theÂ other only 4. In how many ways can they travel?
A.	126
B.	240
C.	120
D.	260
Answer» B. 240

Discussion

225.	A standard deck of playing cards has 13 spades. How many ways can these 13 spades beÂ arranged?
A.	13!
B.	13^2
C.	13^13
D.	2!
Answer» B. 13^2

Discussion

226.	A school has scheduled three volleyball games, two soccer games, and fourÂ basketball games. You have a ticket allowing you to attend three of the games. In howÂ many ways can you go to two basketball games and one of the other events?
A.	25
B.	30
C.	50
D.	75
Answer» C. 50

Discussion

227.	A school committee of 5 is to be formed from 12 students.How many committees can be formed if John must be on the committee?
A.	11P4
B.	11C4
C.	11P5
D.	11C5
Answer» C. 11P5

Discussion

228.	A polygon has 44 diagonals, then the number of its sides are ?
A.	13
B.	9
C.	11
D.	7
Answer» D. 7

Discussion

229.	A pizza can have 3 toppings out of possible 7 toppings.How many different pizza's can be made?
A.	49
B.	35
C.	27
D.	25
Answer» C. 27

Discussion

230.	A polygon 7 sides.How many diagonals can be formed?
A.	14
B.	7
C.	15
D.	21
Answer» B. 7

Discussion

231.	A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?
A.	3
B.	5
C.	3!
D.	5!
Answer» C. 3!

Discussion

232.	A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior ?
A.	Â²Â²Câ‚â‚€ + 1
B.	Â²Â²Câ‚‰ + Â¹â°Câ‚
C.	Â²Â²Câ‚â‚€
D.	Â²Â²Câ‚â‚€ - 1
Answer» E.

Discussion

233.	A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group ?
A.	600
B.	610
C.	609
D.	599
Answer» B. 610

Discussion

234.	A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most Â ?
A.	215
B.	268
C.	254
D.	216
Answer» B. 268

Discussion

235.	AÂ 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.	340
B.	210
C.	290
D.	252
Answer» E.

Discussion

236.	A decision committee of 5 members is to be formed out of 4 Actors, 3 Directors and 2 Producers. In how many ways a committee of 2 Actors, 2 Directors and 1 Producer can be formed ?
A.	18
B.	24
C.	36
D.	32
Answer» D. 32

Discussion

237.	A Group consists of 4 couples in which each of the Â 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?
A.	1152
B.	1278
C.	1296
D.	None of these
Answer» B. 1278

Discussion

238.	A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?
A.	142
B.	175
C.	212
D.	253
Answer» E.

Discussion

239.	A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?
A.	123
B.	113
C.	246
D.	945
Answer» D. 945

Discussion

240.	A committee of 5 persons is to be formed from 6 men and 4 women. In howÂ many ways can this be done whenÂ at least 2 women are included ?
A.	196
B.	186
C.	190
D.	200
Answer» C. 190

Discussion

241.	A committee of 4 people is to be formed from a group of 9 people.How many possible committees can be formed?
A.	120
B.	162
C.	126
D.	170
Answer» D. 170

Discussion

242.	A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
A.	1260
B.	210
C.	210 x 6!
D.	1512
Answer» B. 210

Discussion

243.	A coach must choose five starters from a team of 12 players. How many different ways canÂ the coach choose the starters ?
A.	569
B.	729
C.	625
D.	769
Answer» C. 625

Discussion

244.	A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ?_x005F_x000D_ A)Â 11/91_x005F_x000D_ B)Â 4/11_x005F_x000D_ C)Â 1/11_x005F_x000D_ D) 90/91
A.	Option A
B.	Option B
C.	Option C
D.	Option D
Answer» E.

Discussion

245.	A card is drawn from a pack of 52 cards. What is the probability that either card is black or a king?
A.	15/52
B.	17/26
C.	13/17
D.	15/26
Answer» E.

Discussion

246.	A class has 8 football players. A 5-member team and a captain will be selected out of these 8 players. How many different selections can be made ?
A.	210
B.	168
C.	1260
D.	10!/6!
Answer» C. 1260

Discussion

247.	A box contains 5 green, 4 yellow and 3 white marbles. Threemarbles are drawn at random. What is the probability thatthey are not of the same colour ?
A.	40/44
B.	44/41
C.	41/44
D.	40/39
Answer» D. 40/39

Discussion

248.	A certain marathon had 50 people running for first prize, second, and third prize.How many ways are there to correctly guess the first, second, and third place winners?
A.	2
B.	1
C.	4
D.	3
Answer» C. 4

Discussion

249.	A box contains 4 different black balls, 3 different red balls and 5 different blue balls. In how many ways can the balls be selected if every selection must have at least 1 black ball and one red ball ?_x005F_x000D_ A) 24Â -Â 1Â Â _x005F_x000D_ B)Â 2425-1Â Â _x005F_x000D_ C) (24-1)(23-1)25Â Â _x005F_x000D_ D) None
A.	A
B.	B
C.	C
D.	D
Answer» D. D

Discussion

250.	A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow ?
A.	42795
B.	44287
C.	44228
D.	42856
Answer» D. 42856

Discussion

Explore topic-wise MCQs in Arithmetic Ability.

From a deck of 52 cards, a 5 card hand is dealt.How may distinct five card hands are there if the queen of spades and the four of diamonds must be in the hand?

From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?

From a bunch of flowers having 16 red roses and 14 white roses, four flowers have to be selected. In how many different ways can they be selected such that at least one red rose is selected?

From 5 consonants and 4 vowels, how many words can be formed using 3Â consonants and 2 vowels ?

First,second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered.In how many different ways can the prizes be awarded?

Find the value of 'n' for which the nth term of two AP'S:_x005F_x000D_ 15,12,9.... and -15,-13,-11...... are equal?

Find the total numbers greater than 4000 that can be formed with digits 2, 3, 4, 5, 6 no digit being repeated in any number ?

Find the total number of distinct vehicle numbers that can be formed using twoÂ letters followed by two numbers. Letters need to be distinct

Find the sum of the all the numbers formed by the digits 2,4,6 and 8 without repetition. Number may be of any of the form like 2,24,684,4862 ?

Find the number of ways to take 4 people and place them in groups of 3 at a time whereÂ order does not matter?

Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.

Find the number of ways to arrange 6 items in groups of 4 at a time where order matters?

Find the number of ways to take 20 objects and arrange them in groups of 5 at a timeÂ where order does not matter.?

Find the number of ways to draw a straight, (suit does not matter) beginning with a 4 andÂ ending with a 8?

Find the number of ways to arrange 4 people in groups of 3 at a time where orderÂ matters?

Find the number of subsets of the set {1,2,3,4,5,6,7,8,9,10,11} having 4Â elements.

Determine the total number of five-card hands that can be drawn from a deck of 52 cards.

Consider the word ROTOR. Whichever way you read it, from left to right orÂ from right to left, you get the same word. Such a word is known as palindrome. Find theÂ maximum possible number of 5-letter palindromes.

Compute the sum of 4 digit numbers which can be formed with the four digits 1,3,5,7, if each digit is used only once in each arrangement.

A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls.How many councils can have Jason on the council?

A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and theÂ other only 4. In how many ways can they travel?

A standard deck of playing cards has 13 spades. How many ways can these 13 spades beÂ arranged?

A school has scheduled three volleyball games, two soccer games, and fourÂ basketball games. You have a ticket allowing you to attend three of the games. In howÂ many ways can you go to two basketball games and one of the other events?

A school committee of 5 is to be formed from 12 students.How many committees can be formed if John must be on the committee?

A polygon has 44 diagonals, then the number of its sides are ?

A pizza can have 3 toppings out of possible 7 toppings.How many different pizza's can be made?

A polygon 7 sides.How many diagonals can be formed?

A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?

A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior ?

A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group ?

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most Â ?

AÂ 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 decision committee of 5 members is to be formed out of 4 Actors, 3 Directors and 2 Producers. In how many ways a committee of 2 Actors, 2 Directors and 1 Producer can be formed ?

A Group consists of 4 couples in which each of the Â 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?

A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?

A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A committee of 5 persons is to be formed from 6 men and 4 women. In howÂ many ways can this be done whenÂ at least 2 women are included ?

A committee of 4 people is to be formed from a group of 9 people.How many possible committees can be formed?

A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

A coach must choose five starters from a team of 12 players. How many different ways canÂ the coach choose the starters ?

A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ?_x005F_x000D_ A)Â 11/91_x005F_x000D_ B)Â 4/11_x005F_x000D_ C)Â 1/11_x005F_x000D_ D) 90/91

A card is drawn from a pack of 52 cards. What is the probability that either card is black or a king?

A class has 8 football players. A 5-member team and a captain will be selected out of these 8 players. How many different selections can be made ?

A box contains 5 green, 4 yellow and 3 white marbles. Threemarbles are drawn at random. What is the probability thatthey are not of the same colour ?

A certain marathon had 50 people running for first prize, second, and third prize.How many ways are there to correctly guess the first, second, and third place winners?

A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow ?