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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 635 · 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.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  2. 2.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
  3. 3.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 240 (d) 25
  4. 4.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  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) 30 (d) 35
  6. 6.4 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) 16 (b) 8 (c) 6 (d) 12
  7. 7.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) 8 (b) 12 (c) 24 (d) 18
  8. 8.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) 18 (c) 9 (d) 12
  9. 9.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 81 (d) 72
  10. 10.5 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) 15 (b) 20 (c) 10 (d) 7
  11. 11.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  12. 12.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  13. 13.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 55 (d) 45
  14. 14.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  15. 15.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) 10 (c) 32 (d) 16
  16. 16.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 210 (d) 105
  17. 17.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 156 (d) 91
  18. 18.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  19. 19.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 15 (d) 25
  20. 20.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  21. 21.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
  22. 22.6 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) 10 (b) 30 (c) 24 (d) 48
  23. 23.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) 84 (c) 48 (d) 42
  24. 24.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 36 (d) 30
  25. 25.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 7 (c) 24 (d) 12
  26. 26.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 90 (d) 20
  27. 27.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 196 (c) 182 (d) 91
  28. 28.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 24 (d) 132
  29. 29.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 15 (c) 10 (d) 20
  30. 30.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 121 (d) 55
  31. 31.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 42 (c) 84 (d) 48
  32. 32.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
  33. 33.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) 42 (b) 10 (c) 21 (d) 28
  34. 34.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
  35. 35.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 120 (d) 210
  36. 36.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 42 (d) 28
  37. 37.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 110 (c) 22 (d) 121
  38. 38.4 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) 32 (c) 16 (d) 8
  39. 39.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
  40. 40.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 28 (c) 16 (d) 56

Answer key

  1. 120
  2. 10
  3. 120
  4. 120
  5. 30
  6. 8
  7. 12
  8. 9
  9. 72
  10. 10
  11. 24
  12. 6
  13. 45
  14. 24
  15. 16
  16. 105
  17. 78
  18. 24
  19. 10
  20. 24
  21. 28
  22. 24
  23. 42
  24. 15
  25. 12
  26. 45
  27. 91
  28. 132
  29. 10
  30. 110
  31. 42
  32. 120
  33. 21
  34. 6
  35. 105
  36. 21
  37. 55
  38. 16
  39. 30
  40. 56

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