Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 470 · 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.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 12 (d) 24
2. 2.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 64 (c) 56 (d) 36
3. 3.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 18 (d) 72
4. 4.8 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) 64 (b) 32 (c) 12 (d) 40
5. 5.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 169 (d) 78
6. 6.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 30 (d) 15
7. 7.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) 5 (b) 9 (c) 12 (d) 6
8. 8.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 21 (d) 15
9. 9.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 55 (d) 110
10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 12 (d) 48
11. 11.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
12. 12.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 42 (c) 49 (d) 21
13. 13.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
14. 14.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
15. 15.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
16. 16.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
17. 17.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 15 (d) 10
18. 18.6 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) 36 (b) 9 (c) 24 (d) 18
19. 19.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
20. 20.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
21. 21.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
22. 22.4 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) 24 (d) 48
23. 23.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) 60 (b) 36 (c) 11 (d) 30
24. 24.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 36 (d) 81
25. 25.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 18 (c) 24 (d) 12
26. 26.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) 32 (b) 28 (c) 11 (d) 56
27. 27.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
28. 28.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 25 (c) 10 (d) 50
29. 29.4 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) 16 (b) 24 (c) 12 (d) 7
30. 30.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
31. 31.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 28 (c) 56 (d) 64
32. 32.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 25 (c) 40 (d) 20
33. 33.4 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) 40 (b) 24 (c) 9 (d) 20
34. 34.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 12 (d) 24
35. 35.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 36 (c) 45 (d) 72
36. 36.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 24 (c) 48 (d) 16
37. 37.5 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) 40 (b) 25 (c) 20 (d) 9
38. 38.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 196 (c) 105 (d) 182
39. 39.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) 12 (b) 42 (c) 35 (d) 70
40. 40.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 182 (d) 91

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