Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 279 · 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.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
2. 2.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
3. 3.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 24 (d) 144
4. 4.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 48 (d) 12
5. 5.8 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) 48 (b) 56 (c) 96 (d) 14
6. 6.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
7. 7.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 21 (d) 42
8. 8.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 66 (d) 132
9. 9.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
10. 10.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) 48 (b) 56 (c) 14 (d) 96
11. 11.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 91 (d) 78
12. 12.7 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) 21 (b) 14 (c) 9 (d) 28
13. 13.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) 32 (b) 24 (c) 10 (d) 16
14. 14.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 20 (d) 240
15. 15.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) 7 (c) 15 (d) 12
16. 16.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 49 (d) 28
17. 17.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 18 (c) 81 (d) 36
18. 18.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 112 (c) 15 (d) 56
19. 19.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120
20. 20.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 22 (d) 121
21. 21.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
22. 22.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
23. 23.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
24. 24.There are 7 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) 35 (b) 42 (c) 12 (d) 70
25. 25.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
26. 26.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
27. 27.There are 5 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) 25 (b) 40 (c) 20 (d) 9
28. 28.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 120 (d) 240
29. 29.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
30. 30.8 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) 11 (b) 24 (c) 48 (d) 32
31. 31.6 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) 18 (b) 24 (c) 36 (d) 9
32. 32.7 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) 98 (b) 49 (c) 56 (d) 14
33. 33.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 81 (d) 18
34. 34.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) 15 (b) 18 (c) 8 (d) 30
35. 35.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
36. 36.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 64 (d) 36
37. 37.There are 8 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) 112 (b) 15 (c) 64 (d) 56
38. 38.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 48 (d) 12
39. 39.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
40. 40.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12

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