Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 885 · 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 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
2. 2.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 45 (d) 90
3. 3.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 72 (d) 81
4. 4.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
5. 5.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
6. 6.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 36 (d) 12
7. 7.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 10 (c) 30 (d) 48
8. 8.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 120 (c) 210 (d) 105
9. 9.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
10. 10.3 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) 36 (b) 18 (c) 21 (d) 9
11. 11.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 30 (d) 15
12. 12.7 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) 28 (b) 56 (c) 35 (d) 11
13. 13.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 210 (d) 105
14. 14.8 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
15. 15.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 55 (d) 66
16. 16.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
17. 17.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 22 (c) 121 (d) 110
18. 18.There are 6 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) 13 (b) 84 (c) 48 (d) 42
19. 19.3 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) 6 (b) 18 (c) 9 (d) 12
20. 20.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 36 (c) 72 (d) 45
21. 21.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 132 (d) 144
22. 22.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 16 (d) 28
23. 23.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 56 (d) 64
24. 24.8 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) 56 (c) 48 (d) 96
25. 25.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 240 (d) 20
26. 26.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) 15 (b) 112 (c) 56 (d) 64
27. 27.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 20 (d) 240
28. 28.3 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
29. 29.8 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) 32 (b) 11 (c) 24 (d) 48
30. 30.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 12 (d) 24
31. 31.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
32. 32.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
33. 33.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
34. 34.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
35. 35.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
36. 36.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 18 (c) 12 (d) 6
37. 37.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) 24 (d) 9
38. 38.7 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) 28 (b) 42 (c) 21 (d) 10
39. 39.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
40. 40.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) 9 (b) 5 (c) 12 (d) 6

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