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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 349 · 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 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 25 (d) 21
  2. 2.8 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) 16 (d) 24
  3. 3.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
  4. 4.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  5. 5.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 28 (d) 64
  6. 6.5 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) 70 (b) 35 (c) 40 (d) 12
  7. 7.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 56 (c) 16 (d) 64
  8. 8.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  9. 9.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 105 (d) 120
  10. 10.6 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) 30 (b) 48 (c) 24 (d) 10
  11. 11.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  12. 12.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 9 (d) 12
  13. 13.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  14. 14.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 78 (c) 156 (d) 169
  15. 15.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 66 (d) 24
  16. 16.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) 48 (c) 84 (d) 42
  17. 17.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  18. 18.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
  19. 19.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
  20. 20.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 78 (d) 66
  21. 21.3 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) 12 (b) 7 (c) 24 (d) 15
  22. 22.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) 36 (d) 18
  23. 23.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 90 (d) 100
  24. 24.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
  25. 25.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 25 (d) 10
  26. 26.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  27. 27.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 22 (d) 110
  28. 28.15 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
  29. 29.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 18 (c) 12 (d) 8
  30. 30.7 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) 21 (b) 10 (c) 42 (d) 28
  31. 31.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 196 (c) 91 (d) 182
  32. 32.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) 8 (c) 16 (d) 12
  33. 33.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 42 (d) 21
  34. 34.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 10 (d) 20
  35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  36. 36.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 42 (c) 49 (d) 21
  37. 37.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 182 (d) 196
  38. 38.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 90 (d) 45
  39. 39.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 56 (d) 64
  40. 40.There are 8 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) 64 (b) 56 (c) 112 (d) 15

Answer key

  1. 20
  2. 16
  3. 66
  4. 24
  5. 28
  6. 35
  7. 28
  8. 120
  9. 105
  10. 24
  11. 6
  12. 6
  13. 120
  14. 78
  15. 132
  16. 42
  17. 6
  18. 15
  19. 21
  20. 66
  21. 12
  22. 72
  23. 90
  24. 10
  25. 10
  26. 120
  27. 110
  28. 105
  29. 12
  30. 21
  31. 91
  32. 8
  33. 21
  34. 10
  35. 24
  36. 21
  37. 91
  38. 45
  39. 56
  40. 56

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