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permutations and combinations MCQs

Practise focused permutations and combinations questions with marked answers for exam preparation and subject revision.

permutations and combinations Mcqs

1. A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
0

A. 20

B. 54

C. 42

D. 60

2. Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
0

A. 6

B. 8

C. 7

D. 5

3. How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
0

A. 120

B. 60

C. 360

D. 240

4. The number of new words that can be formed by rearranging the letters of the word ALIVE is__________?
0

A. 119

B. 23

C. 24

D. 120

5. A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order?
0

A. 20

B. 15

C. 25

D. 10

6. A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
0

A. 15

B. 63

C. 1023

D. 511

7. A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
0

A. 108

B. 12

C. 21

D. 9

8. In how many different ways can the letters of the word MATHEMATICS be arranged so that the vowels always come together?
0

A. 10080

B. 4989600

C. 120960

D. None of these

9. How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
0

A. 60

B. 300

C. 360

D. 180

10. A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted?
0

A. 30

B. 11

C. 14

D. 20

11. A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played?
0

A. 12

B. 42

C. 36

D. 48

12. 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?
0

A. C??

B. C? + ?C?

C. C?? 1

D. C?? + 1

13. Three flags each of different colours are available for a military exercise, Using these flags different codes can be generated by waving <br> I. Single flag of different colours <br> II. Any two flags in a different sequence of colours. <br> III. three flags in a different sequence of colours. <br> The maximum number of codes that can be generated is.
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A. 15

B. 6

C. 18

D. 9

14. Find the number of ways of arranging the letters of the word MATERIAL such that all the vowels in the word are to come together?
0

A. 2160

B. 1860

C. 720

D. 1440

15. There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?
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A. 30

B. 18

C. 15

D. 24

16. Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?
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A. Three

B. Cannot be determined

C. Zero

D. One

17. In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
0

A. 400

B. 600

C. 500

D. 20

18. What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
0

A. 60

B. 20

C. 100

D. 30

19. 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 5 seniors and 5 juniors?
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A. C? * ?C?

B. C? * 10

C. C? * 10

D. 12 * ?C?

20. A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number of possible combinations of selectees is___________?
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A. 12

B. 4

C. 18

D. None of these

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