Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 584 · 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 CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
2. 2.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 36 (d) 15
3. 3.7 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) 70 (b) 35 (c) 12 (d) 42
4. 4.3 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) 8 (b) 18 (c) 15 (d) 30
5. 5.13 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
6. 6.6 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) 48 (c) 24 (d) 10
7. 7.8 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) 24 (c) 11 (d) 48
8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
9. 9.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 30 (d) 36
10. 10.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 72 (d) 81
11. 11.3 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) 18 (b) 21 (c) 36 (d) 9
12. 12.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
13. 13.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) 24 (b) 10 (c) 48 (d) 28
14. 14.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 9 (c) 12 (d) 6
15. 15.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 210 (d) 225
16. 16.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 15 (d) 36
17. 17.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 25 (c) 15 (d) 20
18. 18.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
19. 19.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
20. 20.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 105 (d) 196
21. 21.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 120 (d) 240
22. 22.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 24 (d) 66
23. 23.There are 7 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) 14 (b) 9 (c) 28 (d) 21
24. 24.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 45 (d) 90
25. 25.7 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) 9 (b) 28 (c) 14 (d) 21
26. 26.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) 96 (b) 56 (c) 48 (d) 14
27. 27.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) 35 (c) 11 (d) 30
28. 28.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 64 (d) 56
29. 29.6 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) 36 (b) 24 (c) 9 (d) 18
30. 30.There are 8 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) 40 (b) 32 (c) 12 (d) 64
31. 31.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) 72 (b) 36 (c) 42 (d) 12
32. 32.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 24 (c) 48 (d) 12
33. 33.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 240 (c) 20 (d) 120
34. 34.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 10 (d) 20
35. 35.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 90 (c) 100 (d) 45
36. 36.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 36 (d) 72
37. 37.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
38. 38.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
39. 39.5 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) 7 (b) 10 (c) 15 (d) 20
40. 40.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 21 (d) 14

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