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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 98 · 40 questions
TalentJR

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).

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  1. 1.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  2. 2.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) 9 (b) 21 (c) 28 (d) 14
  3. 3.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 66 (d) 121
  4. 4.7 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) 10 (b) 28 (c) 42 (d) 21
  5. 5.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
  6. 6.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) 25 (b) 10 (c) 30 (d) 50
  7. 7.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 21 (d) 42
  8. 8.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 169 (c) 156 (d) 91
  9. 9.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) 48 (b) 24 (c) 28 (d) 10
  10. 10.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 156 (d) 78
  11. 11.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 30 (c) 11 (d) 35
  12. 12.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  13. 13.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 25 (d) 10
  14. 14.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  15. 15.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 30 (d) 15
  16. 16.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 28 (c) 56 (d) 36
  17. 17.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
  18. 18.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  19. 19.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
  20. 20.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
  21. 21.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  22. 22.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) 18 (b) 36 (c) 24 (d) 9
  23. 23.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  24. 24.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) 7 (b) 16 (c) 12 (d) 24
  25. 25.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 36 (c) 21 (d) 15
  26. 26.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  27. 27.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  28. 28.6 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) 24 (b) 30 (c) 48 (d) 10
  29. 29.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 144 (d) 66
  30. 30.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  31. 31.3 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) 7 (b) 12 (c) 24 (d) 15
  32. 32.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 28 (d) 42
  33. 33.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 36 (d) 64
  34. 34.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) 7 (b) 24 (c) 15 (d) 12
  35. 35.There are 8 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) 56 (b) 96 (c) 14 (d) 48
  36. 36.3 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) 42 (b) 10 (c) 24 (d) 21
  37. 37.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
  38. 38.There are 6 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 60 (b) 36 (c) 30 (d) 11
  39. 39.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 21 (d) 14
  40. 40.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 16 (d) 12

Answer key

  1. 120
  2. 14
  3. 55
  4. 21
  5. 45
  6. 25
  7. 42
  8. 78
  9. 24
  10. 78
  11. 30
  12. 24
  13. 20
  14. 10
  15. 15
  16. 28
  17. 8
  18. 6
  19. 72
  20. 15
  21. 120
  22. 18
  23. 120
  24. 12
  25. 15
  26. 24
  27. 24
  28. 24
  29. 66
  30. 6
  31. 12
  32. 21
  33. 28
  34. 12
  35. 48
  36. 21
  37. 66
  38. 30
  39. 21
  40. 24

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