Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 359 · 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. 1.4 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) 40 (b) 24 (c) 9 (d) 20
2. 2.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
3. 3.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
4. 4.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 25 (d) 240
5. 5.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 48 (c) 40 (d) 80
6. 6.7 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) 10 (b) 42 (c) 28 (d) 21
7. 7.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
8. 8.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 12 (d) 36
9. 9.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 12 (d) 16
10. 10.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 16 (d) 48
11. 11.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 25 (d) 20
12. 12.There are 3 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) 42 (b) 24 (c) 10 (d) 21
13. 13.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 12 (c) 35 (d) 40
14. 14.There are 6 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) 12 (b) 18 (c) 8 (d) 24
15. 15.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) 10 (b) 7 (c) 15 (d) 20
16. 16.4 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) 16 (b) 7 (c) 12 (d) 24
17. 17.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) 10 (b) 24 (c) 48 (d) 28
18. 18.8 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) 32 (b) 10 (c) 16 (d) 24
19. 19.7 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) 35 (b) 12 (c) 70 (d) 42
20. 20.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 55 (c) 121 (d) 22
21. 21.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 225 (d) 120
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. 23.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 91 (c) 196 (d) 182
24. 24.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
25. 25.8 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) 80 (b) 48 (c) 40 (d) 13
26. 26.There are 3 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) 18 (b) 8 (c) 15 (d) 30
27. 27.13 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
28. 28.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 78 (d) 169
29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
30. 30.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 25 (d) 11
31. 31.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 25 (d) 240
32. 32.There are 7 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) 28 (b) 10 (c) 42 (d) 21
33. 33.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 56 (c) 28 (d) 11
34. 34.5 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
35. 35.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 16 (d) 24
37. 37.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 91 (c) 196 (d) 105
38. 38.3 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) 7 (b) 15 (c) 12 (d) 24
39. 39.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 20 (d) 90
40. 40.6 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) 10 (c) 24 (d) 48

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