JEE Main - Simple applications of permutations and combinations Online Test (MCQ Quiz)

1. How many ways can the letters of the word 'SUCCESS' be arranged?

A) 840 B) 420 C) 1680 D) 5040

2. In how many ways can a committee of 3 men and 2 women be formed from 7 men and 5 women?

A) 441 B) 210 C) 840 D) 1260

3. How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition?

A) 60 B) 120 C) 15 D) 20

4. How many ways can 5 boys and 3 girls be seated in a row so that no two girls sit together?

A) 720 B) 1440 C) 4320 D) 5040

5. A bag contains 5 red balls and 7 white balls. In how many ways can 3 balls be drawn such that 2 are red and 1 is white?

A) 70 B) 35 C) 105 D) 210

6. How many permutations are there of the letters of the word 'ENGINEERING'?

A) 3628800 B) 277200 C) 138600 D) 69300

7. How many ways can the letters of the word 'ALGEBRA' be arranged if the vowels must always be together?

A) 120 B) 720 C) 24 D) 144

8. Find the number of ways to select 4 balls from a collection of 6 red balls, 4 blue balls and 2 green balls, if exactly 2 must be blue.

A) 120 B) 210 C) 84 D) 168

9. How many different signals can be made by hoisting 6 different colored flags one above the other?

A) 720 B) 64 C) 36 D) 120

10. How many ways can the letters of the word 'MISSISSIPPI' be arranged?

A) 34650 B) 11550 C) 39916800 D) 69300

11. In how many ways can a team of 11 players be chosen from 15 players?

A) 15C4 B) 15C11 C) 15P4 D) 15P11

12. How many ways can 5 different books be arranged on a shelf?

A) 25 B) 120 C) 10 D) 5

13. How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5 without repetition?

A) 360 B) 300 C) 120 D) 600

14. How many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?

A) 2520 B) 1680 C) 840 D) 3360

15. From a group of 6 boys and 4 girls, how many ways can we select a committee of 3 people such that there is at least one girl?

A) 76 B) 84 C) 120 D) 100

16. How many ways can the letters of the word 'BANANA' be arranged?

A) 60 B) 120 C) 720 D) 30

17. How many ways can 4 different mathematics books, 3 different physics books, and 2 different chemistry books be arranged on a shelf so that all books of the same subject are together?

A) 1296 B) 296 C) 36288 D) 8640

18. How many 3-letter words can be formed from the letters of the word 'EQUATION'?

A) 336 B) 504 C) 168 D) 1008

19. How many ways can 5 people be seated in a row of 7 chairs?

A) 2520 B) 210 C) 120 D) 42

20. How many ways can a president, vice-president, and treasurer be selected from a club of 10 members?

A) 720 B) 120 C) 100 D) 30

21. How many ways can the letters of the word 'SUCCESS' be arranged such that all the S's are together?

A) 120 B) 60 C) 24 D) 30

22. A committee of 5 members is to be formed from 6 men and 4 women. In how many ways can this be done if the committee must have exactly 3 men?

A) 120 B) 60 C) 20 D) 15

23. How many distinct permutations are there of the letters in the word 'STATISTICS'?

A) 50400 B) 151200 C) 5040 D) 138600

24. How many ways can 5 boys and 5 girls be arranged in a row so that they alternate?

A) 14400 B) 28800 C) 57600 D) 120

25. How many ways can 3 prizes be awarded to 5 students, if no student can receive more than one prize?

A) 15 B) 60 C) 125 D) 10

26. How many ways can the letters of the word 'PARALLEL' be arranged?

A) 5040 B) 10080 C) 40320 D) 840

27. How many ways can a committee of 4 be chosen from 10 people?

A) 210 B) 5040 C) 100 D) 24

28. How many 5-digit palindromic numbers can be formed using the digits 1, 2, 3, 4, 5?

A) 125 B) 25 C) 625 D) 3125

29. How many ways can the letters of the word 'ASSASSINATION' be arranged?

A) 138600 B) 40320 C) 10810800 D) 39916800

30. How many ways can 7 different flowers be arranged in a garland?

A) 5040 B) 720 C) 2520 D) 6

31. How many ways can a committee of 3 men and 3 women be formed from 7 men and 6 women?

A) 420 B) 1260 C) 540 D) 350

32. How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 if repetition is allowed?

A) 360 B) 15625 C) 1296 D) 64

33. How many ways can the letters of the word 'CORRESPONDENCE' be arranged?

A) 11! B) 11! / (2! * 2! * 2! * 2!) C) 11! / (2! * 2! * 2!) D) 11! / (3! * 2! * 2!)

34. How many ways can 5 identical red balls and 3 identical blue balls be arranged in a row?

A) 56 B) 8 C) 15 D) 1

35. In how many ways can 5 books on Mathematics, 4 books on Physics, and 3 books on Chemistry be arranged on a shelf if books of the same subject must be kept together?

A) 12! B) 6 * 4! * 3! C) 12 * 5! * 4! * 3! D) 5! * 4! * 3!

36. How many ways can the letters of the word 'DAUGHTER' be arranged if the vowels must always be together?

A) 720 B) 1440 C) 5040 D) 4320

37. How many ways can a committee of 5 be selected from 6 men and 5 women so as to include at least 3 men?

A) 186 B) 156 C) 126 D) 90

38. How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5 if digits can be repeated?

A) 100 B) 120 C) 150 D) 210

39. How many ways can the letters of the word 'MATHEMATICS' be arranged?

A) 11! / (2! * 2! * 2!) B) 11! / (2! * 3!) C) 11! / (2! * 2!) D) 11! / (3! * 2!)

40. How many ways can 4 boys and 3 girls be seated in a row so that all the girls sit together?

A) 720 B) 1440 C) 5040 D) 24

41. How many ways can 6 different items be distributed among 3 people if each person must receive at least one item?

A) 729 B) 27 C) 540 D) 18

42. How many ways can the letters of the word 'ARRANGEMENT' be arranged?

A) 11! / (2! * 2! * 2!) B) 11! / (2! * 2!) C) 11! / (3! * 2!) D) 11! / (2! * 2! * 2! * 2!)

43. How many ways can a committee of 4 be formed from 5 men and 6 women if the committee must have exactly 2 men?

A) 150 B) 120 C) 100 D) 90

44. How many distinct permutations are there of the letters of the word 'TALLAHASSEE'?

A) 10! / (2! * 3! * 2!) B) 10! / (3! * 2! * 2!) C) 10! / (3! * 2! * 2! * 2!) D) 10! / (2! * 2! * 2!)

45. How many ways can 3 boys and 3 girls be seated in a row so that they alternate?

A) 72 B) 144 C) 36 D) 6

46. How many ways can 5 distinct prizes be distributed among 4 students, if each student can receive any number of prizes?

A) 1024 B) 625 C) 54 D) 20

47. How many ways can the letters of the word 'BOOKKEEPER' be arranged?

A) 10! / (2! * 2! * 3!) B) 10! / (2! * 3! * 2!) C) 10! / (2! * 2! * 2!) D) 10! / (3! * 2! * 2!)

48. How many ways can a committee of 5 be selected from 7 men and 5 women so that it has exactly 3 women?

A) 350 B) 210 C) 175 D) 105

49. How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5 without repetition?

A) 600 B) 720 C) 6000 D) 540

50. How many ways can the letters of the word 'COMMITTEE' be arranged?

A) 9! / (2! * 2!) B) 9! / (2! * 2! * 2!) C) 9! / (3! * 2! * 2!) D) 9! / (2! * 3!)

Simple applications of permutations and combinations - Online Test

Test Results