Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 85 · 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. 1.5 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) 20 (b) 8 (c) 15 (d) 30
2. 2.There are 3 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) 30 (b) 8 (c) 15 (d) 18
3. 3.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
4. 4.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 40 (c) 20 (d) 24
5. 5.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 32 (c) 40 (d) 64
6. 6.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) 15 (b) 112 (c) 64 (d) 56
7. 7.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 66 (d) 55
8. 8.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 6 (d) 9
9. 9.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 20 (d) 120
10. 10.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
11. 11.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 20 (d) 100
12. 12.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 66 (d) 24
13. 13.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 28 (d) 42
14. 14.There are 5 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) 50 (b) 10 (c) 25 (d) 30
15. 15.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 100 (d) 45
16. 16.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
17. 17.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 120 (d) 20
18. 18.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
19. 19.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
20. 20.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) 6 (c) 5 (d) 9
21. 21.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 64 (d) 56
22. 22.7 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) 28 (b) 14 (c) 21 (d) 9
23. 23.There are 5 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) 8 (b) 15 (c) 20 (d) 30
24. 24.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 56 (d) 28
25. 25.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) 56 (c) 28 (d) 11
26. 26.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 24 (d) 12
27. 27.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15
28. 28.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 144 (d) 78
29. 29.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 45 (c) 55 (d) 100
30. 30.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
31. 31.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 12 (c) 35 (d) 42
32. 32.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 120 (d) 105
33. 33.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 25 (d) 20
34. 34.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
36. 36.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
37. 37.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 30 (d) 21
38. 38.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) 24 (b) 8 (c) 18 (d) 12
39. 39.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) 28 (b) 10 (c) 48 (d) 24
40. 40.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 110 (d) 55

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