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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 651 · 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. 1.11 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
  2. 2.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 91 (d) 196
  3. 3.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78
  4. 4.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) 15 (c) 30 (d) 18
  5. 5.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) 24 (b) 15 (c) 7 (d) 12
  6. 6.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  7. 7.4 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) 16 (b) 12 (c) 7 (d) 24
  8. 8.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 81 (c) 72 (d) 45
  9. 9.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  10. 10.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  11. 11.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 42 (c) 21 (d) 10
  12. 12.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 132 (d) 144
  13. 13.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 30 (c) 36 (d) 21
  14. 14.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 105 (d) 120
  15. 15.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) 12 (b) 9 (c) 6 (d) 18
  16. 16.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  17. 17.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
  18. 18.4 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) 20 (b) 9 (c) 24 (d) 40
  19. 19.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 28 (c) 64 (d) 56
  20. 20.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 105 (d) 210
  21. 21.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
  22. 22.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  23. 23.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
  24. 24.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 144 (d) 24
  25. 25.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 10 (c) 25 (d) 21
  26. 26.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  27. 27.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 13 (c) 40 (d) 80
  28. 28.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 64 (d) 16
  29. 29.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 55 (d) 121
  30. 30.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
  31. 31.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 78 (c) 169 (d) 91
  32. 32.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 25 (b) 20 (c) 40 (d) 9
  33. 33.7 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) 35 (b) 70 (c) 12 (d) 42
  34. 34.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) 24 (b) 32 (c) 11 (d) 48
  35. 35.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 49 (d) 21
  36. 36.4 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) 48 (b) 24 (c) 28 (d) 10
  37. 37.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 20 (d) 100
  38. 38.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  39. 39.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 28 (d) 64
  40. 40.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 110 (d) 55

Answer key

  1. 55
  2. 91
  3. 66
  4. 15
  5. 12
  6. 10
  7. 12
  8. 36
  9. 120
  10. 24
  11. 21
  12. 132
  13. 15
  14. 105
  15. 9
  16. 6
  17. 6
  18. 20
  19. 56
  20. 105
  21. 30
  22. 24
  23. 21
  24. 66
  25. 20
  26. 120
  27. 40
  28. 28
  29. 55
  30. 72
  31. 78
  32. 20
  33. 35
  34. 24
  35. 21
  36. 24
  37. 45
  38. 120
  39. 28
  40. 55

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