546 + Mcqs in Permutation and Combination McqOptions

1.	In how many ways can 5 members be selected out of 10 members, so that two particular members must always be excluded?
A.	52
B.	56
C.	60
D.	64
Answer» C. 60

Discussion

2.	In how many ways can the letters of the word 'COMPUTER' be arranged so that the vowels are always together.
A.	5!3!
B.	8!
C.	6!2!
D.	6!3!
Answer» E.

Discussion

3.	In how many ways can the letters of the word BIHAR be arranged where each such letter appears exactly once?
A.	120
B.	130
C.	110
D.	100
Answer» B. 130

Discussion

4.	In a box, there are eight yellow and four black balls. If three balls are drawn at random, what is the probability that two are yellow and one black?
A.	1/16
B.	28/55
C.	3/8
D.	8C2/4C1
Answer» C. 3/8

Discussion

5.	A bag contains 5 red and 4 black balls. Four balls are drawn at random. In how many ways can we draw, so that there are exactly 2 red balls
A.	48
B.	24
C.	36
D.	60
Answer» E.

Discussion

6.	How many arrangements can be made using all the letter of the word DAUGHTER exactly once each so that the vowels always come together?
A.	0234
B.	3420
C.	2340
D.	4320
Answer» E.

Discussion

7.	In how many ways can a necklace with 8 beads of different colors be made?
A.	5,040
B.	2,880
C.	2,520
D.	1,440
Answer» D. 1,440

Discussion

8.	How many 3-digit even numbers can be formed using 1, 2, 3, 4, 6, 7 digits without repeating them?
A.	60
B.	40
C.	20
D.	30
Answer» B. 40

Discussion

9.	Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:
A.	9
B.	24
C.	6
D.	18
Answer» E.

Discussion

10.	A group of 260 children are seated in n rows for a group photo session. Each row contains three less children than the row in front of it. Which of the following number of rows is not possible?
A.	3
B.	4
C.	5
D.	6
Answer» E.

Discussion

11.	In how many ways can four children be made to stand in a line such that two of them, A and B are always together ?
A.	6
B.	12
C.	18
D.	24
Answer» C. 18

Discussion

12.	If 2nCn-1 : (2n - 1) Cn = 5 : 3, then what is the value of n?
A.	2
B.	3
C.	4
D.	5
Answer» E.

Discussion

13.	In an examination there are three multiple choice questions and each question has 4 choices. The number of ways in which a student can fail to get all answer correct is-
A.	1
B.	7
C.	2
D.	3
Answer» E.

Discussion

14.	In how many different ways can the letters the word FORMULATE be arranged?
A.	100
B.	0320
C.	53420
D.	62880
E.	one of these
Answer» E. one of these

Discussion

15.	In how many different ways can letters of the word OFFICES be arranged?
A.	520
B.	040
C.	850
D.	680
E.	one of these
Answer» B. 040

Discussion

16.	In how many different ways can the letters of the word ‘BAKERY’ be arranged?
A.	400
B.	005
C.	20
D.	040
E.	one of these
Answer» D. 040

Discussion

17.	In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?
A.	20
B.	8
C.	2
D.	68
E.	one of these
Answer» D. 68

Discussion

18.	In how many ways can a committee of 4 people be chosen out of 8 people?
A.	2
B.	0
C.	10
D.	26
E.	one of these
Answer» C. 10

Discussion

19.	In how many different ways can the letters of the word OPERATE be arranged?
A.	4
B.	60
C.	0160
D.	0320
E.	one of these
Answer» D. 0320

Discussion

20.	In how many different ways can the letters of the word ABSENTEE be arranged?
A.	12
B.	720
C.	740
D.	0320
E.	one of these
Answer» C. 740

Discussion

21.	In how many different ways can the letters of the word SMART be arranged?
A.	5
B.	0
C.	80
D.	00
E.	one of these
Answer» F.

Discussion

22.	In how many different ways can the letters of the word TOTAL be arranged?
A.	5
B.	0
C.	2
D.	20
E.	one of these
Answer» C. 2

Discussion

23.	In how many ways can the letters of the word MATHEMATICS be arranged so that all the vowels always come together?
A.	0080
B.	20960
C.	989600
D.	1160
E.	one of these
Answer» C. 989600

Discussion

24.	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 at least 1 man?
A.	15
B.	20
C.	25
D.	40
E.	one of these
Answer» D. 40

Discussion

25.	In how many different ways can the letters of the word SOFTWARE be arranged in such a way that the vowels always come together?
A.	20
B.	60
C.	440
D.	3440
E.	320
Answer» F.

Discussion

26.	There are six teachers. Out of them two are primary teachers and two are secondary teachers. They are to stand in a row, so as the primary teachers, middle teachers and secondary teachers are always in a set . The number of ways in which they can do so, is-
A.	2
B.	8
C.	4
D.	one of these
Answer» C. 4

Discussion

27.	In how many ways can the letters of the word ‘MOMENT’ be arranged?
A.	60
B.	0
C.	20
D.	20
Answer» B. 0

Discussion

28.	In how many different ways can the letters of the word MACHINE be arranged so that the vowels may occupy only the odd positions?
A.	10
B.	76
C.	44
D.	728
E.	456
Answer» C. 44

Discussion

29.	In how many different ways can the letters of the word AUCTION be arranged in such a way that the vowels always come together?
A.	0
B.	8
C.	44
D.	76
E.	one of these
Answer» E. one of these

Discussion

30.	A select group of 4 is to be formed from 8 men and 6 women in such a way that the group must have at least 1 women. In how many different ways can it be done ?
A.	64
B.	28
C.	31
D.	001
E.	one of these
Answer» D. 001

Discussion

31.	In how many different way can the letters of the word WEDDING be arranged?
A.	500
B.	520
C.	000
D.	040
E.	ONE OF THESE
Answer» C. 000

Discussion

32.	In how many different ways can the letters of the word RIDDLED be arranged?
A.	40
B.	680
C.	520
D.	040
E.	one of these
Answer» B. 680

Discussion

33.	In how many different ways can the letters of the word DISPLAY be arranged?
A.	20
B.	140
C.	520
D.	040
E.	one of these
Answer» E. one of these

Discussion

34.	In how many different ways can the letters of the word JUDGE be arranged in such a way that the vowels always come together?
A.	8
B.	20
C.	24
D.	60
E.	one of these
Answer» B. 20

Discussion

35.	In how many different ways can the letters of the word CORPORATION be arranged so that the vowels may occupy only the odd positions?
A.	10
B.	440
C.	880
D.	0400
E.	one of these
Answer» E. one of these

Discussion

36.	In how many different ways can the letters of the word ENGINEERING be arranged?
A.	77200
B.	2400
C.	9300
D.	3100
E.	one of these
Answer» B. 2400

Discussion

37.	How many factors of 25 × 36 × 52 are perfect squares?
A.	0
B.	4
C.	0
D.	6
Answer» C. 0

Discussion

38.	How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4 if repetition of digits is allowed?
A.	99
B.	00
C.	75
D.	76
E.	01
Answer» E. 01

Discussion

39.	How many positive integers 'n' can be form using the digits 3, 4, 4, 5, 6, 6, 7 if we want 'n' to exceed 60,00,000?
A.	20
B.	60
C.	40
D.	20
Answer» D. 20

Discussion

40.	While packing for a business trip Mr. Debashis has packed 3 pairs of shoes, 4 pants, 3 half-pants,6 shirts, 3 sweater and 2 jackets. The outfit is defined as consisting of a pair of shoes, a choice of "lower wear" (either a pant or a half-pant), a choice of "upper wear" (it could be a shirt or a sweater or both) and finally he may or may not choose to wear a jacket. How many different outfits are possible?
A.	67
B.	821
C.	43
D.	701
Answer» E.

Discussion

41.	A student is required to answer 6 out of 10 questions divided into two groups each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he make the choice?
A.	10
B.	50
C.	00
D.	00
Answer» E.

Discussion

42.	How many numbers are there between 100 and 1000 such that at least one of their digits is 6?
A.	00
B.	25
C.	52
D.	20
Answer» D. 20

Discussion

43.	In a cricket match if a batsman score 0, 1, 2, 3, 4 or 6 runs of a ball, then find the number or different sequences in which he can score exactly 30 runs of an over. Assume that an over consists of only 6 balls and there were no extra and no run outs.
A.	6
B.	1
C.	6
D.	5
Answer» C. 6

Discussion

44.	Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
A.	10
B.	9
C.	× 28
D.	one of these
Answer» C. × 28

Discussion

45.	The number of ways which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same is:
A.	514
B.	512
C.	024
D.	028
Answer» C. 024

Discussion

46.	There are five comics numbered from 1 to 5. In how many ways can they be arranged, so that part-1 and part-3 are never together?
A.	8
B.	2
C.	20
D.	10
Answer» C. 20

Discussion

47.	In how many ways can 6 green toys and 6 red toys be arranged, such that 2 particular red toys are never together whereas 2 particular green toys are always together?
A.	1! × 2!
B.	! × 90
C.	× 10!
D.	8 × 10!
Answer» E.

Discussion

48.	Six boxes are numbered 1, 2, 3, 4, 5 and 6. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. find the total number of ways of placing the balls.
A.	5
B.	0
C.	1
D.	6
Answer» D. 6

Discussion

49.	There are 20 couples in a party. Every person greets every person except his or her spouse. People of the same sex shake hands and those of opposite sex greet each other with a Namaste (It means bringing one's own palms together and raising them to the chest level). What is the total number of handshakes and Namaste's in the party?
A.	60
B.	140
C.	80
D.	20
Answer» C. 80

Discussion

50.	How many natural numbers less than a lakh can be formed with the digits 0,6 and 9?
A.	42
B.	43
C.	28
D.	29
Answer» B. 43

Discussion

Explore topic-wise MCQs in Testing Subject.

In how many ways can 5 members be selected out of 10 members, so that two particular members must always be excluded?

In how many ways can the letters of the word 'COMPUTER' be arranged so that the vowels are always together.

In how many ways can the letters of the word BIHAR be arranged where each such letter appears exactly once?

In a box, there are eight yellow and four black balls. If three balls are drawn at random, what is the probability that two are yellow and one black?

A bag contains 5 red and 4 black balls. Four balls are drawn at random. In how many ways can we draw, so that there are exactly 2 red balls

How many arrangements can be made using all the letter of the word DAUGHTER exactly once each so that the vowels always come together?

In how many ways can a necklace with 8 beads of different colors be made?

How many 3-digit even numbers can be formed using 1, 2, 3, 4, 6, 7 digits without repeating them?

Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

A group of 260 children are seated in n rows for a group photo session. Each row contains three less children than the row in front of it. Which of the following number of rows is not possible?

In how many ways can four children be made to stand in a line such that two of them, A and B are always together ?

If 2nCn-1 : (2n - 1) Cn = 5 : 3, then what is the value of n?

In an examination there are three multiple choice questions and each question has 4 choices. The number of ways in which a student can fail to get all answer correct is-

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

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

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

In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?

In how many ways can a committee of 4 people be chosen out of 8 people?

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

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

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

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

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

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 at least 1 man?

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

There are six teachers. Out of them two are primary teachers and two are secondary teachers. They are to stand in a row, so as the primary teachers, middle teachers and secondary teachers are always in a set . The number of ways in which they can do so, is-

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

In how many different ways can the letters of the word MACHINE be arranged so that the vowels may occupy only the odd positions?

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

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

In how many different way can the letters of the word WEDDING be arranged?

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

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

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

In how many different ways can the letters of the word CORPORATION be arranged so that the vowels may occupy only the odd positions?

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

How many factors of 25 × 36 × 52 are perfect squares?

How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4 if repetition of digits is allowed?

How many positive integers 'n' can be form using the digits 3, 4, 4, 5, 6, 6, 7 if we want 'n' to exceed 60,00,000?

A student is required to answer 6 out of 10 questions divided into two groups each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he make the choice?

How many numbers are there between 100 and 1000 such that at least one of their digits is 6?

In a cricket match if a batsman score 0, 1, 2, 3, 4 or 6 runs of a ball, then find the number or different sequences in which he can score exactly 30 runs of an over. Assume that an over consists of only 6 balls and there were no extra and no run outs.

Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

The number of ways which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same is:

There are five comics numbered from 1 to 5. In how many ways can they be arranged, so that part-1 and part-3 are never together?

In how many ways can 6 green toys and 6 red toys be arranged, such that 2 particular red toys are never together whereas 2 particular green toys are always together?

Six boxes are numbered 1, 2, 3, 4, 5 and 6. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. find the total number of ways of placing the balls.

How many natural numbers less than a lakh can be formed with the digits 0,6 and 9?