Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 194 · 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 captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
2. 2.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 30 (c) 21 (d) 36
3. 3.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 15 (d) 10
4. 4.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 55 (d) 121
5. 5.There are 5 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) 30 (b) 35 (c) 60 (d) 11
6. 6.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
7. 7.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 18 (c) 81 (d) 36
8. 8.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
10. 10.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
11. 11.8 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) 112 (b) 15 (c) 64 (d) 56
12. 12.11 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
13. 13.6 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) 24 (b) 10 (c) 30 (d) 48
14. 14.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
15. 15.5 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) 60 (b) 11 (c) 30 (d) 35
16. 16.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 15 (c) 12 (d) 24
17. 17.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
18. 18.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 15 (c) 64 (d) 112
19. 19.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
20. 20.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 120 (d) 20
21. 21.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 42 (d) 14
22. 22.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 91 (c) 182 (d) 105
23. 23.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 20 (d) 25
24. 24.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 120 (c) 105 (d) 210
25. 25.3 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) 18 (b) 9 (c) 36 (d) 21
26. 26.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 91 (c) 169 (d) 78
27. 27.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 49 (d) 42
28. 28.There are 3 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) 21 (b) 36 (c) 18 (d) 9
29. 29.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 18 (d) 36
30. 30.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) 21 (b) 28 (c) 14 (d) 9
31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
32. 32.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
33. 33.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 42 (d) 49
34. 34.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 40 (c) 12 (d) 70
35. 35.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 30 (d) 36
36. 36.There are 4 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) 32 (b) 16 (c) 20 (d) 8
37. 37.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 12 (d) 30
38. 38.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 8 (b) 12 (c) 16 (d) 6
39. 39.8 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) 11 (b) 32 (c) 24 (d) 48
40. 40.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) 48 (b) 80 (c) 13 (d) 40

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