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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 400 · 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. 1.13 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
  2. 2.14 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
  3. 3.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 7 (d) 12
  4. 4.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 10 (d) 25
  5. 5.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  6. 6.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 55 (d) 66
  7. 7.4 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) 20 (b) 8 (c) 16 (d) 32
  8. 8.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
  9. 9.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 13 (c) 42 (d) 49
  10. 10.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 15 (c) 30 (d) 36
  11. 11.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  12. 12.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 28 (d) 64
  13. 13.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  14. 14.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  15. 15.There are 3 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) 21 (b) 18 (c) 36 (d) 9
  16. 16.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
  17. 17.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 56 (d) 28
  18. 18.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  19. 19.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 48 (d) 12
  20. 20.8 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) 15 (b) 112 (c) 64 (d) 56
  21. 21.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
  22. 22.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 49 (d) 28
  23. 23.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
  24. 24.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 144 (d) 66
  25. 25.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 72 (d) 36
  26. 26.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30
  27. 27.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  28. 28.4 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) 12 (b) 6 (c) 16 (d) 8
  29. 29.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 64 (c) 56 (d) 28
  30. 30.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  31. 31.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) 11 (d) 56
  32. 32.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 225 (d) 210
  33. 33.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 81 (c) 18 (d) 36
  34. 34.There are 8 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) 10 (b) 24 (c) 32 (d) 16
  35. 35.There are 4 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) 32 (b) 16 (c) 8 (d) 20
  36. 36.There are 5 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) 40 (b) 35 (c) 70 (d) 12
  37. 37.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 78 (d) 144
  38. 38.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  39. 39.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 45 (d) 100
  40. 40.7 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) 49 (b) 14 (c) 98 (d) 56

Answer key

  1. 78
  2. 91
  3. 12
  4. 20
  5. 24
  6. 55
  7. 16
  8. 105
  9. 42
  10. 15
  11. 120
  12. 28
  13. 120
  14. 24
  15. 18
  16. 21
  17. 28
  18. 120
  19. 24
  20. 56
  21. 56
  22. 21
  23. 55
  24. 66
  25. 36
  26. 30
  27. 45
  28. 8
  29. 28
  30. 6
  31. 28
  32. 105
  33. 72
  34. 16
  35. 16
  36. 35
  37. 66
  38. 6
  39. 45
  40. 49

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