Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 10 · 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.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 96 (c) 56 (d) 48
3. 3.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
4. 4.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 32 (c) 24 (d) 11
5. 5.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 72 (d) 18
6. 6.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 15 (d) 21
7. 7.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169
8. 8.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 10 (c) 28 (d) 24
9. 9.6 T-shirts and 4 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) 30 (c) 48 (d) 24
10. 10.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 16 (c) 7 (d) 24
11. 11.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 90 (d) 45
12. 12.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
13. 13.7 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) 10 (b) 21 (c) 28 (d) 42
14. 14.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 12 (c) 36 (d) 72
15. 15.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
17. 17.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
18. 18.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 64 (b) 15 (c) 56 (d) 112
19. 19.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 36 (d) 12
20. 20.4 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) 9 (b) 40 (c) 20 (d) 24
21. 21.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 35 (c) 11 (d) 56
22. 22.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) 35 (b) 28 (c) 56 (d) 11
23. 23.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 15 (d) 30
24. 24.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 30 (c) 60 (d) 11
25. 25.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 25 (d) 120
26. 26.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 56 (d) 28
27. 27.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 48 (c) 13 (d) 80
28. 28.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
29. 29.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 24 (d) 48
30. 30.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
31. 31.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 28 (c) 48 (d) 10
32. 32.6 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) 24 (b) 36 (c) 18 (d) 9
33. 33.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 56 (c) 49 (d) 98
34. 34.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 45 (d) 90
35. 35.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 12 (d) 24
36. 36.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 36 (d) 15
37. 37.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 9 (c) 12 (d) 18
38. 38.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
39. 39.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 78 (c) 169 (d) 91
40. 40.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 35 (c) 70 (d) 12

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