Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 2 · 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. 1.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 45 (d) 55
2. 2.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
3. 3.4 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) 28 (b) 48 (c) 10 (d) 24
4. 4.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 18 (d) 72
5. 5.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 48 (d) 16
6. 6.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
7. 7.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 12 (d) 48
8. 8.5 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) 50 (b) 30 (c) 25 (d) 10
9. 9.There are 5 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) 8 (b) 30 (c) 20 (d) 15
10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
11. 11.4 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) 11 (b) 56 (c) 32 (d) 28
12. 12.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 45 (d) 90
13. 13.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 8 (c) 12 (d) 6
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) 6 (b) 9 (c) 12 (d) 5
15. 15.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 56 (d) 28
16. 16.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
17. 17.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 25 (d) 120
18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
19. 19.There are 7 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) 42 (b) 49 (c) 84 (d) 13
20. 20.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) 64 (b) 56 (c) 15 (d) 112
21. 21.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 121 (d) 110
22. 22.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
23. 23.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 156 (c) 91 (d) 169
24. 24.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
25. 25.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 25 (d) 20
26. 26.There are 4 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) 12 (b) 16 (c) 7 (d) 24
27. 27.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
28. 28.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 30 (d) 12
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.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
31. 31.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 49 (d) 28
32. 32.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 55 (d) 66
33. 33.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
34. 34.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 48 (c) 28 (d) 24
35. 35.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
36. 36.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 48 (d) 12
37. 37.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 45 (d) 81
38. 38.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 24 (c) 18 (d) 12
39. 39.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 15 (c) 30 (d) 21
40. 40.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 144 (d) 24

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