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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 79 · 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).

NameDateTime takenScore ___ / 40
  1. 1.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 28 (d) 21
  2. 2.4 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) 8 (b) 16 (c) 32 (d) 20
  3. 3.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) 10 (c) 21 (d) 42
  4. 4.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  5. 5.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 55 (d) 66
  6. 6.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 30 (d) 36
  7. 7.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 20 (d) 10
  8. 8.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 28 (c) 42 (d) 10
  9. 9.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 42 (d) 14
  10. 10.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 45 (d) 100
  11. 11.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) 12 (c) 18 (d) 8
  12. 12.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 12 (c) 72 (d) 36
  13. 13.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 56 (c) 64 (d) 16
  14. 14.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 18 (c) 30 (d) 8
  15. 15.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) 15 (b) 8 (c) 30 (d) 18
  16. 16.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 20 (d) 100
  17. 17.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  18. 18.There are 4 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) 28 (b) 48 (c) 10 (d) 24
  19. 19.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  20. 20.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  21. 21.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  22. 22.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  23. 23.There are 7 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) 42 (b) 10 (c) 21 (d) 28
  24. 24.3 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) 12 (b) 18 (c) 9 (d) 6
  25. 25.6 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) 11 (d) 30
  26. 26.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 21 (d) 42
  27. 27.6 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
  28. 28.3 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) 18 (b) 36 (c) 21 (d) 9
  29. 29.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 196 (d) 91
  30. 30.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 56 (d) 28
  31. 31.7 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) 28 (b) 9 (c) 14 (d) 21
  32. 32.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
  33. 33.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
  34. 34.3 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) 15 (b) 18 (c) 30 (d) 8
  35. 35.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 169 (c) 78 (d) 156
  36. 36.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  37. 37.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  38. 38.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) 16 (c) 6 (d) 8
  39. 39.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  40. 40.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) 25 (b) 30 (c) 50 (d) 10

Answer key

  1. 21
  2. 16
  3. 21
  4. 120
  5. 55
  6. 15
  7. 10
  8. 21
  9. 42
  10. 90
  11. 12
  12. 36
  13. 56
  14. 15
  15. 15
  16. 45
  17. 120
  18. 24
  19. 24
  20. 6
  21. 24
  22. 6
  23. 21
  24. 9
  25. 30
  26. 21
  27. 12
  28. 18
  29. 91
  30. 28
  31. 14
  32. 15
  33. 10
  34. 15
  35. 78
  36. 120
  37. 120
  38. 8
  39. 6
  40. 25

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