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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 688 · 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) 25 (c) 21 (d) 20
  2. 2.There are 3 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) 5 (c) 9 (d) 6
  3. 3.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
  4. 4.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 30 (d) 36
  5. 5.5 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
  6. 6.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) 48 (b) 24 (c) 11 (d) 32
  7. 7.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 110 (c) 55 (d) 121
  8. 8.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 18 (c) 9 (d) 36
  9. 9.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 14 (d) 49
  10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 16 (d) 12
  11. 11.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
  12. 12.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
  13. 13.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 21 (d) 30
  14. 14.15 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
  15. 15.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
  16. 16.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 105 (d) 91
  17. 17.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
  18. 18.4 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) 8 (b) 12 (c) 16 (d) 6
  19. 19.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
  20. 20.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 169 (d) 78
  21. 21.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 156 (c) 91 (d) 169
  22. 22.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 240 (d) 25
  23. 23.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  24. 24.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  25. 25.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 105 (d) 210
  26. 26.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 100 (d) 45
  27. 27.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  28. 28.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  29. 29.There are 6 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) 30 (b) 36 (c) 11 (d) 60
  30. 30.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 49 (d) 28
  31. 31.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  32. 32.3 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) 9 (b) 12 (c) 18 (d) 6
  33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
  34. 34.8 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) 64 (b) 40 (c) 32 (d) 12
  35. 35.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  36. 36.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 36 (d) 56
  37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  38. 38.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 36 (d) 72
  39. 39.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 56 (d) 28
  40. 40.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 132 (c) 66 (d) 24

Answer key

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

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