Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 75 · 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 team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 64 (d) 28
2. 2.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 28 (d) 64
3. 3.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) 32 (b) 24 (c) 16 (d) 10
4. 4.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66
5. 5.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 24 (d) 48
6. 6.There are 8 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) 40 (b) 13 (c) 80 (d) 48
7. 7.8 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) 40 (c) 32 (d) 12
8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 12 (d) 48
9. 9.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 105 (d) 182
10. 10.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) 42 (b) 36 (c) 72 (d) 12
11. 11.7 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) 21 (b) 10 (c) 28 (d) 42
12. 12.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 25 (d) 20
13. 13.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 16 (d) 48
14. 14.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 55 (d) 66
15. 15.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
16. 16.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
17. 17.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 100 (d) 90
18. 18.There are 5 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) 20 (b) 15 (c) 10 (d) 7
19. 19.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) 40 (b) 9 (c) 20 (d) 25
20. 20.There are 4 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) 11 (b) 32 (c) 28 (d) 56
21. 21.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 12 (d) 24
22. 22.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 56 (d) 64
23. 23.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) 10 (b) 24 (c) 21 (d) 42
24. 24.There are 6 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) 36 (c) 18 (d) 24
25. 25.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 10 (c) 15 (d) 25
26. 26.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78
27. 27.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 55 (d) 45
28. 28.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
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) 12 (b) 7 (c) 24 (d) 15
30. 30.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 25 (d) 240
31. 31.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 30 (d) 21
32. 32.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 12 (d) 36
33. 33.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 72 (c) 36 (d) 18
34. 34.8 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) 16 (b) 24 (c) 10 (d) 32
35. 35.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 20 (c) 90 (d) 100
36. 36.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 132 (d) 24
37. 37.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
39. 39.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
40. 40.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) 55 (d) 22

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