Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 152 · 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 a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
2. 2.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 91 (c) 182 (d) 196
3. 3.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 22 (d) 121
4. 4.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 48 (d) 24
5. 5.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
6. 6.5 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) 30 (b) 25 (c) 10 (d) 50
7. 7.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
8. 8.3 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) 18 (b) 8 (c) 30 (d) 15
9. 9.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 42 (d) 21
10. 10.8 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
11. 11.There are 3 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) 9 (b) 6 (c) 18 (d) 12
12. 12.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 30 (c) 48 (d) 24
13. 13.8 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) 48 (b) 32 (c) 11 (d) 24
14. 14.There are 4 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) 6 (b) 8 (c) 16 (d) 12
15. 15.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) 24 (b) 12 (c) 8 (d) 18
16. 16.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 36 (d) 45
17. 17.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 169 (d) 156
18. 18.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
19. 19.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
20. 20.4 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) 32 (b) 28 (c) 56 (d) 11
21. 21.3 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) 24 (c) 7 (d) 15
22. 22.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
23. 23.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 72 (c) 36 (d) 18
24. 24.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
25. 25.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
26. 26.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 25 (d) 10
27. 27.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 100 (d) 45
28. 28.A canteen sells 5 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 50 (b) 25 (c) 10 (d) 30
29. 29.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 78 (d) 91
30. 30.6 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) 72 (b) 36 (c) 12 (d) 42
31. 31.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
32. 32.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 90 (d) 45
33. 33.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) 36 (b) 24 (c) 18 (d) 9
34. 34.6 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) 36 (b) 60 (c) 30 (d) 11
35. 35.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 210 (c) 105 (d) 120
36. 36.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 55 (d) 121
37. 37.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
38. 38.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 12 (c) 7 (d) 24
39. 39.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
40. 40.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 12 (d) 9

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