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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 1 · 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. 1.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
  2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  3. 3.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 55 (d) 110
  4. 4.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 66 (c) 144 (d) 78
  5. 5.3 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) 5 (b) 6 (c) 12 (d) 9
  6. 6.3 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) 18 (b) 12 (c) 9 (d) 6
  7. 7.4 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) 6 (c) 12 (d) 8
  8. 8.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  9. 9.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) 100 (d) 90
  10. 10.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 10 (d) 25
  11. 11.6 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) 48 (b) 24 (c) 10 (d) 30
  12. 12.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 80 (c) 40 (d) 48
  13. 13.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 78 (c) 91 (d) 169
  14. 14.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  15. 15.4 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) 16 (b) 20 (c) 8 (d) 32
  16. 16.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  17. 17.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 3 (d) 12
  18. 18.3 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) 18 (b) 30 (c) 15 (d) 8
  19. 19.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 156 (c) 169 (d) 78
  20. 20.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 21 (c) 10 (d) 42
  21. 21.There are 7 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) 42 (b) 35 (c) 70 (d) 12
  22. 22.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) 9 (d) 5
  23. 23.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 110 (d) 121
  24. 24.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
  25. 25.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 45 (d) 20
  26. 26.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) 21 (d) 42
  27. 27.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 36 (d) 72
  28. 28.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 55 (c) 100 (d) 90
  29. 29.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
  30. 30.8 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
  31. 31.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) 28 (b) 21 (c) 9 (d) 14
  32. 32.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  33. 33.5 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) 10 (b) 7 (c) 15 (d) 20
  34. 34.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 225 (d) 210
  35. 35.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  36. 36.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
  37. 37.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  38. 38.4 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) 24 (b) 9 (c) 40 (d) 20
  39. 39.6 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
  40. 40.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36

Answer key

  1. 45
  2. 24
  3. 110
  4. 66
  5. 6
  6. 9
  7. 8
  8. 120
  9. 90
  10. 20
  11. 24
  12. 40
  13. 78
  14. 120
  15. 16
  16. 6
  17. 6
  18. 15
  19. 78
  20. 21
  21. 35
  22. 6
  23. 55
  24. 66
  25. 45
  26. 42
  27. 36
  28. 45
  29. 21
  30. 28
  31. 14
  32. 24
  33. 10
  34. 105
  35. 24
  36. 21
  37. 24
  38. 20
  39. 15
  40. 15

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