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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 280 · 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 PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  2. 2.15 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
  3. 3.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 132 (d) 144
  4. 4.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  5. 5.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 66 (c) 55 (d) 121
  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) 6 (b) 18 (c) 12 (d) 9
  7. 7.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 12 (c) 36 (d) 15
  8. 8.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 10 (d) 15
  9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  10. 10.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) 8 (c) 15 (d) 30
  11. 11.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 55 (d) 45
  12. 12.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
  13. 13.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 66 (d) 121
  14. 14.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
  15. 15.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
  16. 16.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  17. 17.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 48 (c) 32 (d) 24
  18. 18.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  19. 19.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
  20. 20.7 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
  21. 21.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 64 (c) 12 (d) 40
  22. 22.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
  23. 23.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 91 (d) 105
  24. 24.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  25. 25.7 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) 12 (b) 70 (c) 42 (d) 35
  26. 26.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) 18 (b) 12 (c) 9 (d) 6
  27. 27.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  28. 28.There are 8 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) 32 (b) 11 (c) 48 (d) 24
  29. 29.3 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) 9 (b) 18 (c) 36 (d) 21
  30. 30.6 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) 48 (b) 42 (c) 13 (d) 84
  31. 31.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 36 (d) 64
  32. 32.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
  33. 33.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 72 (d) 36
  34. 34.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) 12 (b) 8 (c) 16 (d) 6
  35. 35.6 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) 12 (b) 24 (c) 8 (d) 18
  36. 36.There are 5 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) 70 (b) 40 (c) 35 (d) 12
  37. 37.5 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) 20 (c) 15 (d) 7
  38. 38.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) 48 (b) 10 (c) 28 (d) 24
  39. 39.3 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) 10 (b) 42 (c) 24 (d) 21
  40. 40.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) 35 (b) 40 (c) 70 (d) 12

Answer key

  1. 6
  2. 105
  3. 66
  4. 24
  5. 55
  6. 9
  7. 30
  8. 10
  9. 24
  10. 15
  11. 45
  12. 56
  13. 55
  14. 105
  15. 120
  16. 24
  17. 24
  18. 6
  19. 90
  20. 21
  21. 32
  22. 24
  23. 91
  24. 6
  25. 35
  26. 9
  27. 120
  28. 24
  29. 18
  30. 42
  31. 28
  32. 20
  33. 36
  34. 8
  35. 12
  36. 35
  37. 10
  38. 24
  39. 21
  40. 35

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