Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 21 · 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 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 110 (d) 121
2. 2.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 15 (d) 12
3. 3.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
4. 4.6 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) 30 (b) 24 (c) 10 (d) 48
5. 5.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 21 (d) 10
6. 6.3 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) 30 (b) 18 (c) 15 (d) 8
7. 7.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
8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
9. 9.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) 48 (b) 10 (c) 24 (d) 28
10. 10.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 21 (c) 30 (d) 36
11. 11.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
12. 12.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120
13. 13.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 105 (d) 225
14. 14.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
15. 15.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 21 (d) 42
16. 16.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 30 (d) 12
17. 17.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 20 (d) 45
18. 18.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 32 (d) 10
19. 19.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 24 (d) 12
20. 20.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
21. 21.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
22. 22.3 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) 12 (b) 9 (c) 6 (d) 5
23. 23.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
24. 24.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
25. 25.8 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) 14 (b) 96 (c) 56 (d) 48
26. 26.6 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) 30 (b) 11 (c) 60 (d) 36
27. 27.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 110 (c) 121 (d) 55
28. 28.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) 20 (b) 8 (c) 32 (d) 16
29. 29.8 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) 40 (b) 12 (c) 64 (d) 32
30. 30.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
31. 31.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 48 (d) 16
32. 32.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 10 (c) 15 (d) 25
33. 33.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) 20 (b) 40 (c) 9 (d) 24
34. 34.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
35. 35.3 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) 12 (b) 9 (c) 18 (d) 6
36. 36.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) 9 (b) 25 (c) 40 (d) 20
37. 37.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) 32 (b) 12 (c) 40 (d) 64
38. 38.There are 3 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) 24 (b) 15 (c) 7 (d) 12
39. 39.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
40. 40.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 24 (c) 42 (d) 21

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