Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 126 · 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.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) 7 (c) 24 (d) 16
2. 2.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 240 (d) 120
3. 3.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 169 (d) 156
4. 4.4 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) 8 (b) 16 (c) 32 (d) 20
5. 5.There are 8 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) 24 (b) 10 (c) 32 (d) 16
6. 6.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 14 (b) 28 (c) 21 (d) 9
7. 7.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 24 (d) 16
8. 8.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 78 (d) 169
9. 9.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 12 (d) 24
10. 10.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 64 (c) 56 (d) 36
11. 11.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 45 (c) 55 (d) 100
12. 12.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) 30 (d) 11
13. 13.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 9 (d) 12
14. 14.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 132 (d) 66
15. 15.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 210 (d) 120
16. 16.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
17. 17.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 28 (d) 64
18. 18.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 196 (c) 182 (d) 105
19. 19.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) 18 (b) 15 (c) 8 (d) 30
20. 20.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
21. 21.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) 6 (c) 12 (d) 8
22. 22.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 42 (c) 49 (d) 21
23. 23.7 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
24. 24.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 25 (d) 10
25. 25.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
26. 26.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 12 (d) 36
27. 27.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 30 (d) 15
28. 28.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 13 (c) 42 (d) 84
29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 120 (d) 25
30. 30.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 240 (d) 25
31. 31.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
32. 32.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) 18 (b) 36 (c) 9 (d) 24
33. 33.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) 24 (b) 32 (c) 16 (d) 10
34. 34.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 28 (c) 64 (d) 16
35. 35.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25
36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
37. 37.4 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) 8 (c) 16 (d) 6
38. 38.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) 24 (b) 8 (c) 12 (d) 18
39. 39.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) 24 (b) 21 (c) 10 (d) 42
40. 40.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 20 (d) 10

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