Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 51 · 40 questions

How to solve it (Multiply the choices): Multiplication principle: a ways for the first choice and b ways for the next give a × b ways together. n different letters in a row: n × (n − 1) × … × 2 × 1 arrangements. Handshakes, matches or teams of 2 from n (order does not matter): n × (n − 1) ÷ 2. Captain and vice-captain (order matters): n × (n − 1).

1. 1.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
2. 2.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 18 (d) 81
3. 3.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 36 (d) 12
4. 4.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 10 (d) 21
5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 48 (d) 16
6. 6.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 56 (c) 48 (d) 14
7. 7.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
8. 8.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 28 (d) 49
9. 9.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 120 (d) 105
10. 10.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 50 (b) 10 (c) 30 (d) 25
11. 11.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 14 (c) 21 (d) 9
12. 12.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 48 (c) 32 (d) 24
13. 13.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 30 (d) 21
14. 14.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
15. 15.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 12 (c) 6 (d) 9
16. 16.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
17. 17.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 36 (d) 30
18. 18.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 56 (c) 35 (d) 28
19. 19.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 5 (c) 6 (d) 9
20. 20.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 64 (d) 28
21. 21.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 32 (c) 28 (d) 56
22. 22.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 72 (b) 36 (c) 12 (d) 42
23. 23.There are 7 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 70 (b) 42 (c) 12 (d) 35
24. 24.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
25. 25.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 12 (d) 48
26. 26.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 7 (c) 20 (d) 15
27. 27.There are 8 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 16 (b) 32 (c) 24 (d) 10
28. 28.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 20 (d) 240
29. 29.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 36 (d) 72
30. 30.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 16 (c) 12 (d) 7
31. 31.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 55 (c) 121 (d) 22
32. 32.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 66 (c) 110 (d) 121
33. 33.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 144 (d) 132
34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 16 (d) 12
35. 35.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 91 (d) 182
36. 36.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 12 (c) 36 (d) 30
37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
38. 38.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
39. 39.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
40. 40.4 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 28 (c) 48 (d) 24

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