Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 556 · 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.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) 48 (b) 14 (c) 56 (d) 96
2. 2.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) 18 (b) 9 (c) 12 (d) 6
3. 3.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 20 (d) 120
4. 4.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 42 (c) 49 (d) 14
5. 5.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 12 (d) 48
6. 6.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 64 (c) 28 (d) 56
7. 7.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
8. 8.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
9. 9.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
10. 10.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
11. 11.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
12. 12.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
13. 13.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) 14 (b) 21 (c) 9 (d) 28
14. 14.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 24 (d) 48
15. 15.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) 24 (b) 10 (c) 32 (d) 16
16. 16.There are 3 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) 9 (b) 6 (c) 18 (d) 12
17. 17.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) 10 (b) 48 (c) 28 (d) 24
18. 18.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 66 (d) 110
19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 30 (d) 15
20. 20.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 66 (d) 132
21. 21.5 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) 20 (b) 15 (c) 7 (d) 10
22. 22.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 48 (d) 12
23. 23.6 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) 12 (c) 42 (d) 36
24. 24.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
25. 25.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 12 (d) 48
26. 26.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
27. 27.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 66 (d) 78
28. 28.3 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) 9 (b) 5 (c) 6 (d) 12
29. 29.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
30. 30.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) 10 (b) 48 (c) 24 (d) 28
31. 31.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
32. 32.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
34. 34.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 42 (d) 21
35. 35.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 98 (c) 49 (d) 56
36. 36.4 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) 9 (c) 24 (d) 20
37. 37.There are 6 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) 11 (b) 30 (c) 60 (d) 36
38. 38.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 90 (c) 100 (d) 55
39. 39.4 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) 28 (b) 56 (c) 32 (d) 11
40. 40.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 21 (c) 36 (d) 18

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