Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 549 · 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 canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 24 (c) 36 (d) 18
2. 2.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
3. 3.8 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) 96 (b) 14 (c) 56 (d) 48
4. 4.5 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) 60 (b) 35 (c) 11 (d) 30
5. 5.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) 15 (b) 12 (c) 24 (d) 7
6. 6.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
7. 7.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) 24 (b) 10 (c) 16 (d) 32
8. 8.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 15 (c) 18 (d) 30
9. 9.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
10. 10.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 20 (d) 90
11. 11.4 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) 6 (c) 8 (d) 16
12. 12.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
13. 13.7 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) 11 (b) 56 (c) 28 (d) 35
14. 14.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
15. 15.There are 5 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) 60 (b) 11 (c) 35 (d) 30
16. 16.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
17. 17.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 78 (d) 91
18. 18.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 121 (d) 110
19. 19.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 28 (d) 56
20. 20.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
21. 21.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 48 (c) 14 (d) 96
22. 22.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 30 (d) 15
23. 23.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 10 (d) 15
24. 24.There are 8 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) 32 (b) 24 (c) 11 (d) 48
25. 25.15 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
26. 26.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 8 (c) 20 (d) 16
27. 27.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 91 (d) 156
28. 28.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
29. 29.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 10 (c) 25 (d) 20
30. 30.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 15 (d) 12
31. 31.4 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) 7 (c) 24 (d) 16
32. 32.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
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) 9 (b) 40 (c) 20 (d) 24
34. 34.6 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) 24 (b) 10 (c) 30 (d) 48
35. 35.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
36. 36.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
37. 37.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) 7 (b) 15 (c) 10 (d) 20
38. 38.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 21 (d) 42
39. 39.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
40. 40.5 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) 25 (b) 30 (c) 50 (d) 10

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