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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 345 · 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. 1.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 28 (d) 49
  2. 2.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
  3. 3.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  4. 4.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 28 (c) 56 (d) 11
  5. 5.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) 11 (b) 60 (c) 35 (d) 30
  6. 6.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 121 (d) 66
  7. 7.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78
  8. 8.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 5 (c) 9 (d) 6
  9. 9.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 32 (c) 24 (d) 16
  10. 10.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) 9 (c) 40 (d) 20
  11. 11.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 18 (d) 72
  12. 12.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 196 (d) 91
  13. 13.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  15. 15.There are 8 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) 24 (b) 32 (c) 11 (d) 48
  16. 16.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) 24 (c) 42 (d) 21
  17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  18. 18.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 66 (d) 121
  19. 19.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) 28 (b) 21 (c) 14 (d) 9
  20. 20.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  21. 21.9 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
  22. 22.There are 7 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) 9 (b) 14 (c) 21 (d) 28
  23. 23.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  24. 24.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15
  25. 25.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 36 (d) 12
  26. 26.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 120 (d) 105
  27. 27.There are 4 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) 32 (b) 28 (c) 11 (d) 56
  28. 28.7 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) 9 (b) 28 (c) 14 (d) 21
  29. 29.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  30. 30.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) 40 (b) 64 (c) 32 (d) 12
  31. 31.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 25 (d) 15
  32. 32.6 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) 30 (b) 10 (c) 24 (d) 48
  33. 33.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 91 (c) 196 (d) 182
  34. 34.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) 16 (b) 8 (c) 12 (d) 6
  35. 35.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) 10 (c) 30 (d) 24
  36. 36.4 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) 24 (c) 7 (d) 16
  37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  38. 38.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  39. 39.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
  40. 40.5 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) 35 (b) 70 (c) 12 (d) 40

Answer key

  1. 21
  2. 90
  3. 120
  4. 28
  5. 30
  6. 55
  7. 66
  8. 6
  9. 16
  10. 20
  11. 72
  12. 91
  13. 120
  14. 10
  15. 24
  16. 21
  17. 24
  18. 55
  19. 14
  20. 6
  21. 36
  22. 14
  23. 120
  24. 15
  25. 30
  26. 105
  27. 28
  28. 14
  29. 6
  30. 32
  31. 10
  32. 24
  33. 91
  34. 8
  35. 24
  36. 12
  37. 24
  38. 120
  39. 78
  40. 35

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