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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 175 · 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 team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 10 (d) 11
  2. 2.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 120 (d) 20
  3. 3.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  4. 4.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66
  5. 5.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  6. 6.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 28 (d) 64
  7. 7.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 30 (c) 8 (d) 15
  8. 8.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 90 (d) 55
  9. 9.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 100 (d) 20
  10. 10.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 36 (d) 12
  11. 11.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  12. 12.6 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) 30 (d) 11
  13. 13.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 144 (d) 132
  14. 14.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 132 (d) 66
  15. 15.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 14 (c) 9 (d) 28
  16. 16.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) 16 (b) 6 (c) 12 (d) 8
  17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  18. 18.7 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) 49 (b) 84 (c) 42 (d) 13
  19. 19.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 42 (d) 49
  20. 20.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 81 (d) 45
  21. 21.There are 5 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) 10 (b) 30 (c) 50 (d) 25
  22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  23. 23.5 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) 7 (c) 10 (d) 20
  24. 24.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) 40 (b) 70 (c) 12 (d) 35
  25. 25.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 91 (d) 196
  26. 26.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) 16 (b) 20 (c) 32 (d) 8
  27. 27.5 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) 25 (b) 40 (c) 9 (d) 20
  28. 28.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 18 (d) 24
  29. 29.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 21 (d) 15
  30. 30.3 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) 6 (b) 9 (c) 12 (d) 5
  31. 31.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  32. 32.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 225 (d) 105
  33. 33.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  34. 34.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 15 (d) 25
  35. 35.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 81 (d) 36
  36. 36.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  37. 37.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 49 (d) 21
  38. 38.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  39. 39.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 21 (d) 49
  40. 40.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 15 (d) 12

Answer key

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

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