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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?
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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?
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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}
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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__________?
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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?
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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?
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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?
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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?
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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)?
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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?
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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?
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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?
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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?
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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?
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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?
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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
21. Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2?
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A. 81

B. 36

C. 116

D. 91
22. Using all the letters of the word THURSDAY, how many different words can be formed?
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A. 7

B. 7!

C. 8

D. 8!
23. A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
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A. 185

B. 165

C. 205

D. 225

24. Using all the letters of the word NOKIA, how many words can be formed, which begin with N and end with A?
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A. 120

B. 24

C. 3

D. 6
25. The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
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A. 2160

B. 5300

C. 4000

D. 4320
26. Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
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A. 32

B. 29

C. 55

D. 30

27. In how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together?
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A. 2160

B. 120

C. 4320

D. 720
28. A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
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A. 750

B. 450

C. 300

D. 600
29. A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
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A. 300

B. 150

C. 200

D. 250

30. 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?
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A. 9

B. 14

C. 12

D. 18

31. A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
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A. ?C?

B. ?C?

C. C?

D. C?

32. 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?
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A. 40

B. 5040

C. 400

D. 2520

33. The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
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A. 144

B. 120

C. 720

D. 36

34. How many three letter words are formed using the letters of the word TIME?
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A. 20

B. 12

C. 24

D. 16

35. 2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?
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A. 36

B. 60

C. 15

D. 48

36. The number of permutations of the letters of the word MESMERISE is___________?
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A. 9!/(2!)<sup>3</sup>3!

B. 5!/(2!)<sup>2</sup>3!

C. 9!/(2!)<sup>2</sup>(3!)<sup>2</sup>

D. 9!/(2!)23!
37. 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__________?
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A. 215

B. 216

C. 243

D. 729

38. A question paper had 10 questions. Each question could only be answered as true(T) of False(F). Each candidate answered all the questions, Yet no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?
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A. 512

B. 40

C. 1024

D. 20

39. There are 30 people in a group. If all shake hands with one another , how many handshakes are possible?
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A. 870

B. 435

C. 30!

D. 29! + 1

40. A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________?
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A. 5

B. 7

C. 6

D. 18

41. The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________?
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A. (6!)<sup>2</sup>

B. 6! * ?P?

C. 2(6!)

D. 6! * 7

42. 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?
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A. 300

B. 750

C. 900

D. 600
43. In how many ways can live boys and three girls sit in a row such that all boys sit together?
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A. 4800

B. 5760

C. 15000

D. 2880
44. In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
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A. 624

B. 1024

C. 19

D. 120

45. In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?
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A. 480

B. 240

C. 120

D. 360

46. In how many ways can three consonants and two vowels be selected from the letters of the word TRIANGLE?
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A. 30

B. 13

C. 25

D. 40

47. 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?
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A. 63

B. 45

C. 126

D. 90