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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 718 · 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 canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 48 (c) 14 (d) 56
  2. 2.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
  3. 3.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) 18 (b) 12 (c) 6 (d) 9
  4. 4.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
  5. 5.There are 5 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) 25 (b) 50 (c) 30 (d) 10
  6. 6.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  7. 7.There are 6 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) 13 (b) 48 (c) 42 (d) 84
  8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
  9. 9.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  10. 10.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
  11. 11.8 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) 13 (b) 40 (c) 48 (d) 80
  12. 12.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 132 (c) 66 (d) 24
  13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
  14. 14.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  15. 15.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 28 (c) 36 (d) 64
  16. 16.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 10 (d) 15
  17. 17.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) 24 (b) 36 (c) 18 (d) 9
  18. 18.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  19. 19.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  20. 20.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 28 (d) 64
  21. 21.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 91 (c) 182 (d) 105
  22. 22.7 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) 56 (b) 28 (c) 11 (d) 35
  23. 23.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) 56 (b) 32 (c) 28 (d) 11
  24. 24.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  25. 25.6 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) 9 (b) 36 (c) 24 (d) 18
  26. 26.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 182 (d) 196
  27. 27.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  28. 28.6 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) 36 (b) 72 (c) 12 (d) 42
  29. 29.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  30. 30.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 78 (d) 66
  31. 31.6 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) 60 (b) 11 (c) 30 (d) 36
  32. 32.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  33. 33.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 121 (c) 55 (d) 66
  34. 34.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  35. 35.There are 3 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) 6 (c) 5 (d) 9
  36. 36.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
  37. 37.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 121 (d) 55
  38. 38.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 98 (c) 49 (d) 14
  39. 39.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  40. 40.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 91 (c) 156 (d) 169

Answer key

  1. 48
  2. 36
  3. 9
  4. 20
  5. 25
  6. 6
  7. 42
  8. 21
  9. 120
  10. 42
  11. 40
  12. 66
  13. 36
  14. 120
  15. 28
  16. 10
  17. 18
  18. 105
  19. 6
  20. 28
  21. 91
  22. 28
  23. 28
  24. 120
  25. 18
  26. 91
  27. 6
  28. 36
  29. 24
  30. 66
  31. 30
  32. 24
  33. 55
  34. 24
  35. 6
  36. 12
  37. 110
  38. 49
  39. 24
  40. 78

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