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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 264 · 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.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 121 (d) 110
  2. 2.8 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
  3. 3.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 15 (c) 12 (d) 36
  4. 4.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) 10 (b) 32 (c) 24 (d) 16
  5. 5.8 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) 32 (b) 48 (c) 11 (d) 24
  6. 6.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  7. 7.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15
  8. 8.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) 24 (b) 18 (c) 12 (d) 8
  9. 9.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 91 (d) 169
  10. 10.6 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) 72 (b) 42 (c) 12 (d) 36
  11. 11.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 66 (c) 144 (d) 132
  12. 12.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
  13. 13.5 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) 7 (b) 10 (c) 15 (d) 20
  14. 14.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
  15. 15.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 14 (c) 21 (d) 42
  16. 16.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 120 (d) 25
  17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  18. 18.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) 80 (c) 48 (d) 40
  19. 19.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) 48 (b) 42 (c) 13 (d) 84
  20. 20.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 55 (d) 110
  21. 21.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 64 (c) 36 (d) 28
  22. 22.There are 3 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) 8 (b) 30 (c) 18 (d) 15
  23. 23.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  24. 24.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 5 (d) 9
  25. 25.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  26. 26.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 10 (d) 20
  27. 27.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  28. 28.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
  29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 120 (d) 240
  30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
  31. 31.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 210 (d) 225
  32. 32.There are 5 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) 30 (b) 11 (c) 35 (d) 60
  33. 33.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  34. 34.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 196 (c) 182 (d) 105
  35. 35.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
  36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  37. 37.7 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) 70 (b) 35 (c) 42 (d) 12
  38. 38.4 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) 6 (b) 16 (c) 12 (d) 8
  39. 39.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) 12 (c) 8 (d) 16
  40. 40.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 12 (d) 3

Answer key

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

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