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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 429 · 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).

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  1. 1.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  2. 2.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 21 (c) 20 (d) 25
  3. 3.4 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) 8 (b) 16 (c) 12 (d) 6
  4. 4.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) 28 (b) 21 (c) 14 (d) 9
  5. 5.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 36 (d) 15
  6. 6.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
  7. 7.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) 9 (b) 12 (c) 18 (d) 6
  8. 8.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 48 (c) 28 (d) 24
  9. 9.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 6 (d) 3
  10. 10.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 45 (d) 55
  11. 11.6 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) 24 (b) 8 (c) 18 (d) 12
  12. 12.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  13. 13.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  14. 14.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
  15. 15.7 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) 21 (b) 14 (c) 28 (d) 9
  16. 16.8 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) 10 (b) 32 (c) 24 (d) 16
  17. 17.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 66 (d) 55
  18. 18.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  19. 19.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
  20. 20.There are 8 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) 13 (b) 48 (c) 40 (d) 80
  21. 21.There are 7 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) 42 (b) 84 (c) 13 (d) 49
  22. 22.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 91 (d) 196
  23. 23.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45
  24. 24.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 49 (d) 21
  25. 25.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
  26. 26.6 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) 36 (b) 60 (c) 11 (d) 30
  27. 27.In a league, 14 teams each play every other team once. How many matches are played? (a) 196 (b) 91 (c) 105 (d) 182
  28. 28.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  29. 29.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 40 (c) 35 (d) 70
  30. 30.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
  31. 31.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 9 (d) 18
  32. 32.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 10 (c) 25 (d) 11
  33. 33.There are 4 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) 10 (b) 48 (c) 28 (d) 24
  34. 34.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 169 (d) 78
  35. 35.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
  36. 36.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
  37. 37.4 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
  38. 38.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
  39. 39.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  40. 40.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 3 (d) 12

Answer key

  1. 120
  2. 20
  3. 8
  4. 14
  5. 15
  6. 15
  7. 9
  8. 24
  9. 6
  10. 45
  11. 12
  12. 120
  13. 24
  14. 78
  15. 14
  16. 16
  17. 55
  18. 120
  19. 21
  20. 40
  21. 42
  22. 91
  23. 45
  24. 21
  25. 66
  26. 30
  27. 91
  28. 24
  29. 35
  30. 42
  31. 9
  32. 10
  33. 24
  34. 78
  35. 110
  36. 10
  37. 16
  38. 21
  39. 24
  40. 6

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