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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 63 · 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) 21 (b) 42 (c) 28 (d) 49
  2. 2.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  3. 3.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  4. 4.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  5. 5.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
  6. 6.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  7. 7.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 91 (d) 105
  8. 8.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 8 (c) 20 (d) 16
  9. 9.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  10. 10.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 20 (d) 90
  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) 42 (b) 10 (c) 24 (d) 21
  12. 12.There are 7 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) 10 (b) 42 (c) 28 (d) 21
  13. 13.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 36 (d) 72
  14. 14.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  15. 15.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 64 (c) 56 (d) 28
  16. 16.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 16 (d) 64
  17. 17.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) 24 (b) 16 (c) 32 (d) 10
  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 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 24 (d) 66
  20. 20.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
  21. 21.5 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) 20 (b) 15 (c) 7 (d) 10
  22. 22.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 81 (c) 72 (d) 18
  23. 23.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 225 (d) 120
  24. 24.7 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) 42 (b) 70 (c) 35 (d) 12
  25. 25.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) 6 (b) 16 (c) 12 (d) 8
  26. 26.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 21 (c) 49 (d) 42
  27. 27.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) 18 (b) 12 (c) 8 (d) 24
  28. 28.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 15 (d) 25
  29. 29.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  30. 30.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) 11 (b) 36 (c) 60 (d) 30
  31. 31.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 25 (d) 21
  32. 32.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 210 (c) 225 (d) 105
  33. 33.3 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) 5 (b) 6 (c) 9 (d) 12
  34. 34.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
  35. 35.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 64 (c) 40 (d) 12
  36. 36.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 36 (d) 21
  37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  38. 38.There are 6 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) 36 (b) 42 (c) 72 (d) 12
  39. 39.6 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) 42 (b) 36 (c) 12 (d) 72
  40. 40.5 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) 15 (b) 20 (c) 8 (d) 30

Answer key

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

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