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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 436 · 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).

NameDateTime takenScore ___ / 40
  1. 1.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 81 (d) 18
  2. 2.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) 10 (b) 21 (c) 24 (d) 42
  3. 3.4 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) 12 (b) 16 (c) 7 (d) 24
  4. 4.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  5. 5.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 42 (d) 14
  6. 6.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 20 (d) 10
  7. 7.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  8. 8.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 90 (d) 20
  9. 9.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 78 (d) 132
  10. 10.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  11. 11.7 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
  12. 12.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 110 (d) 121
  13. 13.4 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) 28 (b) 24 (c) 48 (d) 10
  14. 14.There are 7 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) 56 (b) 49 (c) 14 (d) 98
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  16. 16.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  17. 17.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  18. 18.There are 6 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) 12 (b) 18 (c) 8 (d) 24
  19. 19.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  20. 20.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  21. 21.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) 30 (b) 35 (c) 11 (d) 60
  22. 22.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) 48 (b) 24 (c) 10 (d) 30
  23. 23.4 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) 8 (b) 12 (c) 16 (d) 6
  24. 24.3 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) 15 (b) 7 (c) 24 (d) 12
  25. 25.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 64 (d) 28
  26. 26.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 28 (c) 56 (d) 36
  27. 27.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) 6 (b) 12 (c) 9 (d) 18
  28. 28.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) 8 (c) 16 (d) 12
  29. 29.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 90 (d) 45
  30. 30.8 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) 96 (b) 14 (c) 56 (d) 48
  31. 31.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  32. 32.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 21 (d) 42
  33. 33.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
  34. 34.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  35. 35.7 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
  36. 36.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 78 (d) 66
  37. 37.6 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) 48 (b) 30 (c) 10 (d) 24
  38. 38.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 24 (d) 144
  39. 39.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 40 (c) 9 (d) 20
  40. 40.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 35 (c) 56 (d) 11

Answer key

  1. 36
  2. 21
  3. 12
  4. 120
  5. 21
  6. 20
  7. 24
  8. 90
  9. 66
  10. 91
  11. 21
  12. 55
  13. 24
  14. 49
  15. 6
  16. 24
  17. 120
  18. 12
  19. 28
  20. 120
  21. 30
  22. 24
  23. 8
  24. 12
  25. 56
  26. 28
  27. 9
  28. 8
  29. 45
  30. 48
  31. 24
  32. 42
  33. 6
  34. 120
  35. 21
  36. 66
  37. 24
  38. 132
  39. 20
  40. 28

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