Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 170 · 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 BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
2. 2.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 30 (d) 36
3. 3.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 144 (d) 66
4. 4.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 56 (d) 16
5. 5.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 81 (c) 45 (d) 72
6. 6.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
7. 7.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) 8 (b) 20 (c) 32 (d) 16
8. 8.There are 7 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) 35 (b) 11 (c) 56 (d) 28
9. 9.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 36 (c) 28 (d) 56
10. 10.3 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) 6 (b) 5 (c) 9 (d) 12
11. 11.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 10 (d) 20
12. 12.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 144 (d) 132
13. 13.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 16 (d) 24
14. 14.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 10 (c) 42 (d) 28
15. 15.7 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) 21 (b) 14 (c) 28 (d) 9
16. 16.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 105 (d) 196
17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 120 (d) 240
18. 18.8 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) 13 (b) 48 (c) 80 (d) 40
19. 19.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 121 (d) 22
20. 20.5 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) 60 (b) 30 (c) 11 (d) 35
21. 21.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
22. 22.6 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) 18 (c) 8 (d) 24
23. 23.4 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) 20 (d) 32
24. 24.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 28 (c) 64 (d) 56
25. 25.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 105 (c) 196 (d) 182
26. 26.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
27. 27.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 81 (d) 72
28. 28.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
29. 29.5 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) 30 (b) 15 (c) 8 (d) 20
30. 30.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 121 (d) 110
31. 31.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) 6 (b) 16 (c) 12 (d) 8
32. 32.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
33. 33.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
34. 34.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 120 (c) 210 (d) 225
35. 35.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
36. 36.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 55 (d) 45
37. 37.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 20 (d) 90
38. 38.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 15 (d) 21
39. 39.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) 20 (b) 30 (c) 15 (d) 8
40. 40.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) 12 (b) 32 (c) 64 (d) 40

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad