OU All In One

Permutations and Combinations questions

Arrangements and selections.

1. How many different arrangements can be made from the letters of "COFFEE"?

  1. 180
  2. 90
  3. 720
  4. 360
Answer

A. 180 6! / 2! (F) × 2! (E) = 180.

2. From 4 men and 4 women, how many teams of 2 men and 2 women can be formed?

  1. 12
  2. 46
  3. 36
  4. 70
Answer

C. 36 4C2 × 4C2 = 6 × 6 = 36.

3. How many different arrangements can be made from the letters of "BALLOON"?

  1. 1260
  2. 2520
  3. 630
  4. 5040
Answer

A. 1260 7! / 2! (L) × 2! (O) = 1260.

4. In how many ways can a committee of 4 be chosen from 10 people?

  1. 120
  2. 5040
  3. 210
  4. 220
Answer

C. 210 10C4 = 10!/(4! × 6!) = 210.

5. In how many ways can the letters of the word "BRICK" be arranged?

  1. 240
  2. 60
  3. 120
  4. 25
Answer

C. 120 5 different letters can be arranged in 5! = 120 ways.

6. How many different arrangements can be made from the letters of "BANANA"?

  1. 30
  2. 120
  3. 66
  4. 60
Answer

D. 60 6! / 3! (A) × 2! (N) = 60.

7. How many different arrangements can be made from the letters of "GOOGLE"?

  1. 360
  2. 720
  3. 90
  4. 180
Answer

D. 180 6! / 2! (G) × 2! (O) = 180.

8. In how many ways can the letters of the word "CHAIR" be arranged?

  1. 24
  2. 120
  3. 25
  4. 240
Answer

B. 120 5 different letters can be arranged in 5! = 120 ways.

9. In how many ways can the letters of the word "SMILE" be arranged?

  1. 24
  2. 120
  3. 60
  4. 240
Answer

B. 120 5 different letters can be arranged in 5! = 120 ways.

10. In how many ways can the letters of the word "TIGER" be arranged?

  1. 240
  2. 120
  3. 24
  4. 25
Answer

B. 120 5 different letters can be arranged in 5! = 120 ways.

11. How many different arrangements can be made from the letters of "LETTER"?

  1. 720
  2. 360
  3. 180
  4. 186
Answer

C. 180 6! / 2! (E) × 2! (T) = 180.

12. How many different arrangements can be made from the letters of "APPLE"?

  1. 60
  2. 30
  3. 120
  4. 65
Answer

A. 60 5! / 2! (P) = 60.

13. In how many ways can the letters of the word "PLANT" be arranged?

  1. 120
  2. 25
  3. 60
  4. 240
Answer

A. 120 5 different letters can be arranged in 5! = 120 ways.

14. In how many ways can the letters of the word "MANGO" be arranged?

  1. 60
  2. 24
  3. 25
  4. 120
Answer

D. 120 5 different letters can be arranged in 5! = 120 ways.

15. In how many ways can the letters of the word "DREAM" be arranged?

  1. 25
  2. 60
  3. 240
  4. 120
Answer

D. 120 5 different letters can be arranged in 5! = 120 ways.

16. In how many ways can the letters of the word "LEMON" be arranged?

  1. 24
  2. 25
  3. 120
  4. 240
Answer

C. 120 5 different letters can be arranged in 5! = 120 ways.

17. From 4 men and 6 women, how many teams of 2 men and 2 women can be formed?

  1. 90
  2. 210
  3. 180
  4. 21
Answer

A. 90 4C2 × 6C2 = 6 × 15 = 90.

18. In how many ways can a committee of 2 be chosen from 11 people?

  1. 165
  2. 66
  3. 110
  4. 55
Answer

D. 55 11C2 = 11!/(2! × 9!) = 55.

19. From 7 men and 3 women, how many teams of 2 men and 2 women can be formed?

  1. 63
  2. 210
  3. 126
  4. 73
Answer

A. 63 7C2 × 3C2 = 21 × 3 = 63.

20. In how many ways can a committee of 4 be chosen from 8 people?

  1. 1680
  2. 78
  3. 56
  4. 70
Answer

D. 70 8C4 = 8!/(4! × 4!) = 70.

21. From 5 men and 4 women, how many teams of 2 men and 2 women can be formed?

  1. 70
  2. 126
  3. 60
  4. 120
Answer

C. 60 5C2 × 4C2 = 10 × 6 = 60.

22. In how many ways can a committee of 3 be chosen from 9 people?

  1. 504
  2. 126
  3. 36
  4. 84
Answer

D. 84 9C3 = 9!/(3! × 6!) = 84.

23. From 4 men and 5 women, how many teams of 2 men and 2 women can be formed?

  1. 60
  2. 126
  3. 120
  4. 16
Answer

A. 60 4C2 × 5C2 = 6 × 10 = 60.

24. In how many ways can a committee of 3 be chosen from 10 people?

  1. 720
  2. 45
  3. 120
  4. 210
Answer

C. 120 10C3 = 10!/(3! × 7!) = 120.

25. From 6 men and 3 women, how many teams of 2 men and 2 women can be formed?

  1. 18
  2. 45
  3. 55
  4. 90
Answer

B. 45 6C2 × 3C2 = 15 × 3 = 45.

26. In how many ways can a committee of 4 be chosen from 7 people?

  1. 35
  2. 840
  3. 21
  4. 42
Answer

A. 35 7C4 = 7!/(4! × 3!) = 35.

27. From 8 men and 6 women, how many teams of 2 men and 2 women can be formed?

  1. 43
  2. 1001
  3. 420
  4. 430
Answer

C. 420 8C2 × 6C2 = 28 × 15 = 420.

28. In how many ways can a committee of 2 be chosen from 6 people?

  1. 30
  2. 21
  3. 15
  4. 6
Answer

C. 15 6C2 = 6!/(2! × 4!) = 15.

29. From 6 men and 5 women, how many teams of 2 men and 2 women can be formed?

  1. 150
  2. 160
  3. 330
  4. 25
Answer

A. 150 6C2 × 5C2 = 15 × 10 = 150.

30. In how many ways can a committee of 3 be chosen from 12 people?

  1. 1320
  2. 220
  3. 495
  4. 232
Answer

B. 220 12C3 = 12!/(3! × 9!) = 220.

31. From 7 men and 4 women, how many teams of 2 men and 2 women can be formed?

  1. 27
  2. 330
  3. 126
  4. 136
Answer

C. 126 7C2 × 4C2 = 21 × 6 = 126.

32. In how many ways can a committee of 3 be chosen from 8 people?

  1. 56
  2. 28
  3. 70
  4. 336
Answer

A. 56 8C3 = 8!/(3! × 5!) = 56.

33. From 6 men and 4 women, how many teams of 2 men and 2 women can be formed?

  1. 180
  2. 100
  3. 90
  4. 21
Answer

C. 90 6C2 × 4C2 = 15 × 6 = 90.

34. In how many ways can a committee of 2 be chosen from 7 people?

  1. 21
  2. 42
  3. 28
  4. 7
Answer

A. 21 7C2 = 7!/(2! × 5!) = 21.

35. From 7 men and 5 women, how many teams of 2 men and 2 women can be formed?

  1. 31
  2. 495
  3. 210
  4. 220
Answer

C. 210 7C2 × 5C2 = 21 × 10 = 210.

36. In how many ways can a committee of 4 be chosen from 12 people?

  1. 507
  2. 11880
  3. 495
  4. 220
Answer

C. 495 12C4 = 12!/(4! × 8!) = 495.

37. From 6 men and 6 women, how many teams of 2 men and 2 women can be formed?

  1. 495
  2. 30
  3. 450
  4. 225
Answer

D. 225 6C2 × 6C2 = 15 × 15 = 225.

38. In how many ways can a committee of 2 be chosen from 12 people?

  1. 66
  2. 78
  3. 132
  4. 220
Answer

A. 66 12C2 = 12!/(2! × 10!) = 66.

39. From 7 men and 6 women, how many teams of 2 men and 2 women can be formed?

  1. 315
  2. 715
  3. 325
  4. 36
Answer

A. 315 7C2 × 6C2 = 21 × 15 = 315.

40. In how many ways can a committee of 3 be chosen from 11 people?

  1. 990
  2. 165
  3. 330
  4. 55
Answer

B. 165 11C3 = 11!/(3! × 8!) = 165.

41. From 8 men and 3 women, how many teams of 2 men and 2 women can be formed?

  1. 84
  2. 94
  3. 330
  4. 31
Answer

A. 84 8C2 × 3C2 = 28 × 3 = 84.

42. In how many ways can a committee of 4 be chosen from 11 people?

  1. 330
  2. 341
  3. 7920
  4. 165
Answer

A. 330 11C4 = 11!/(4! × 7!) = 330.

43. From 4 men and 3 women, how many teams of 2 men and 2 women can be formed?

  1. 28
  2. 18
  3. 9
  4. 36
Answer

B. 18 4C2 × 3C2 = 6 × 3 = 18.

44. In how many ways can a committee of 4 be chosen from 6 people?

  1. 6
  2. 20
  3. 360
  4. 15
Answer

D. 15 6C4 = 6!/(4! × 2!) = 15.

45. From 5 men and 3 women, how many teams of 2 men and 2 women can be formed?

  1. 13
  2. 70
  3. 40
  4. 30
Answer

D. 30 5C2 × 3C2 = 10 × 3 = 30.

46. In how many ways can a committee of 3 be chosen from 6 people?

  1. 26
  2. 15
  3. 20
  4. 120
Answer

C. 20 6C3 = 6!/(3! × 3!) = 20.

47. In how many ways can a committee of 4 be chosen from 9 people?

  1. 84
  2. 3024
  3. 135
  4. 126
Answer

D. 126 9C4 = 9!/(4! × 5!) = 126.

48. In how many ways can a committee of 3 be chosen from 7 people?

  1. 21
  2. 35
  3. 42
  4. 210
Answer

B. 35 7C3 = 7!/(3! × 4!) = 35.

49. In how many ways can a committee of 2 be chosen from 8 people?

  1. 8
  2. 56
  3. 36
  4. 28
Answer

D. 28 8C2 = 8!/(2! × 6!) = 28.

50. In how many ways can a committee of 2 be chosen from 9 people?

  1. 36
  2. 9
  3. 84
  4. 72
Answer

A. 36 9C2 = 9!/(2! × 7!) = 36.

51. How many ways can 3 students be selected from 12 distinct students (order does not matter)?

  1. 220
  2. 200
  3. 218
  4. 232
Answer

A. 220 Use combinations: C(12,3) = 220.

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