Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 401 · 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. 1.8 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) 11 (b) 24 (c) 32 (d) 48
2. 2.There are 5 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) 40 (b) 35 (c) 12 (d) 70
3. 3.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 10 (c) 25 (d) 15
4. 4.14 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
5. 5.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
6. 6.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 45 (d) 90
7. 7.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 20 (d) 25
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.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
10. 10.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) 28 (c) 48 (d) 24
11. 11.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 20 (d) 10
12. 12.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 30 (d) 15
13. 13.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 12 (d) 16
14. 14.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 14 (d) 42
15. 15.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 24 (c) 32 (d) 48
16. 16.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
17. 17.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 15 (c) 12 (d) 36
18. 18.There are 3 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) 7 (b) 12 (c) 24 (d) 15
19. 19.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) 35 (b) 12 (c) 70 (d) 40
20. 20.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
21. 21.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
22. 22.There are 4 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) 16 (b) 8 (c) 20 (d) 32
23. 23.3 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) 12 (b) 7 (c) 24 (d) 15
24. 24.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 225 (d) 105
25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
26. 26.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) 6 (d) 12
27. 27.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
28. 28.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 18 (c) 36 (d) 9
29. 29.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) 30 (b) 8 (c) 20 (d) 15
30. 30.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 132 (d) 24
31. 31.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 25 (d) 20
32. 32.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
33. 33.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
34. 34.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
35. 35.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 15 (d) 25
36. 36.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 30 (c) 15 (d) 21
37. 37.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
38. 38.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 28 (d) 16
39. 39.3 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) 9 (b) 21 (c) 18 (d) 36
40. 40.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) 8 (b) 18 (c) 15 (d) 30

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