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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 186 · 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 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
  2. 2.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 120 (d) 240
  3. 3.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 91 (d) 196
  4. 4.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 25 (d) 20
  5. 5.3 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) 21 (d) 36
  6. 6.6 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) 18 (c) 24 (d) 8
  7. 7.There are 6 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 30 (c) 48 (d) 24
  8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 21 (d) 49
  9. 9.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 12 (c) 7 (d) 16
  10. 10.8 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) 13 (b) 80 (c) 48 (d) 40
  11. 11.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 16 (c) 8 (d) 32
  12. 12.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  13. 13.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 20 (d) 21
  14. 14.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 100 (c) 45 (d) 55
  15. 15.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  16. 16.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  17. 17.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) 9 (b) 21 (c) 36 (d) 18
  18. 18.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 25 (c) 9 (d) 20
  19. 19.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  20. 20.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  21. 21.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 132 (d) 144
  22. 22.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
  23. 23.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  24. 24.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  25. 25.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) 8 (c) 12 (d) 18
  26. 26.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 20 (d) 90
  27. 27.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  28. 28.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 28 (d) 21
  29. 29.8 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) 32 (b) 24 (c) 10 (d) 16
  30. 30.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
  31. 31.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) 12 (b) 32 (c) 40 (d) 64
  32. 32.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
  33. 33.There are 7 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) 98 (b) 49 (c) 14 (d) 56
  34. 34.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
  35. 35.7 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) 28 (b) 21 (c) 42 (d) 10
  36. 36.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 132 (d) 24
  37. 37.6 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) 42 (b) 72 (c) 36 (d) 12
  38. 38.4 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) 6 (b) 8 (c) 16 (d) 12
  39. 39.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 91 (d) 78
  40. 40.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 45 (d) 36

Answer key

  1. 30
  2. 120
  3. 91
  4. 10
  5. 18
  6. 12
  7. 24
  8. 21
  9. 12
  10. 40
  11. 16
  12. 24
  13. 20
  14. 45
  15. 120
  16. 120
  17. 18
  18. 20
  19. 24
  20. 120
  21. 66
  22. 10
  23. 6
  24. 6
  25. 12
  26. 90
  27. 24
  28. 21
  29. 16
  30. 45
  31. 32
  32. 21
  33. 49
  34. 15
  35. 21
  36. 132
  37. 36
  38. 8
  39. 78
  40. 36

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