Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 55 · 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 6 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) 12 (b) 72 (c) 42 (d) 36
2. 2.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 28 (d) 42
3. 3.5 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
4. 4.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 10 (c) 25 (d) 21
5. 5.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) 28 (d) 56
6. 6.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 24 (c) 18 (d) 9
7. 7.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 9 (d) 3
8. 8.There are 3 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) 24 (b) 21 (c) 10 (d) 42
9. 9.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
10. 10.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 121 (c) 22 (d) 55
11. 11.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 66 (d) 24
12. 12.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 14 (c) 42 (d) 49
13. 13.There are 3 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) 12 (b) 5 (c) 9 (d) 6
14. 14.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 25 (d) 20
15. 15.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 45 (d) 100
16. 16.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 105 (c) 182 (d) 91
17. 17.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) 16 (b) 32 (c) 20 (d) 8
18. 18.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 66 (d) 144
19. 19.There are 4 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) 12 (b) 6 (c) 8 (d) 16
20. 20.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
21. 21.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
22. 22.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
23. 23.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 42 (c) 14 (d) 49
24. 24.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 121 (d) 66
25. 25.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) 30 (d) 25
26. 26.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
27. 27.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 100 (d) 90
28. 28.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 81 (c) 45 (d) 72
29. 29.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) 24 (d) 12
30. 30.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 25 (d) 10
31. 31.7 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) 56 (b) 11 (c) 28 (d) 35
32. 32.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 24 (d) 12
33. 33.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 36 (d) 30
34. 34.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 28 (d) 64
35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 240 (d) 20
36. 36.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
37. 37.12 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
38. 38.6 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) 48 (b) 24 (c) 10 (d) 30
39. 39.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 30 (c) 21 (d) 15
40. 40.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 7 (c) 15 (d) 10

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