← Counting and arrangements lesson New set →

Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 73 · 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.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) 12 (b) 6 (c) 18 (d) 9
  2. 2.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 15 (c) 30 (d) 36
  3. 3.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) 30 (b) 50 (c) 10 (d) 25
  4. 4.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 42 (d) 28
  5. 5.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  6. 6.4 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) 24 (c) 16 (d) 7
  7. 7.There are 7 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) 49 (b) 84 (c) 42 (d) 13
  8. 8.14 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
  9. 9.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  10. 10.There are 3 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) 24 (b) 7 (c) 12 (d) 15
  11. 11.3 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) 24 (b) 10 (c) 42 (d) 21
  12. 12.7 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) 42 (b) 10 (c) 21 (d) 28
  13. 13.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
  14. 14.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 45 (d) 20
  15. 15.4 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) 56 (b) 11 (c) 28 (d) 32
  16. 16.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 42 (d) 14
  17. 17.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 15 (d) 30
  18. 18.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) 70 (b) 12 (c) 42 (d) 35
  19. 19.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 56 (d) 28
  20. 20.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  21. 21.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) 42 (b) 10 (c) 21 (d) 24
  22. 22.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 55 (d) 121
  23. 23.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 56 (c) 35 (d) 11
  24. 24.6 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) 13 (b) 48 (c) 84 (d) 42
  25. 25.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 42 (c) 70 (d) 12
  26. 26.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) 16 (c) 7 (d) 12
  27. 27.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) 18 (d) 12
  28. 28.3 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) 15 (b) 24 (c) 12 (d) 7
  29. 29.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
  30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
  31. 31.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 225 (d) 120
  32. 32.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 96 (c) 48 (d) 14
  33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 16 (d) 28
  34. 34.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 66 (d) 144
  35. 35.7 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) 14 (b) 98 (c) 49 (d) 56
  36. 36.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 64 (c) 56 (d) 28
  37. 37.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) 49 (d) 14
  38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  39. 39.4 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) 8 (c) 6 (d) 12
  40. 40.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 25 (d) 120

Answer key

  1. 9
  2. 30
  3. 25
  4. 21
  5. 24
  6. 12
  7. 42
  8. 91
  9. 24
  10. 12
  11. 21
  12. 21
  13. 78
  14. 45
  15. 28
  16. 21
  17. 15
  18. 35
  19. 56
  20. 24
  21. 21
  22. 55
  23. 28
  24. 42
  25. 35
  26. 12
  27. 12
  28. 12
  29. 24
  30. 6
  31. 105
  32. 48
  33. 28
  34. 66
  35. 49
  36. 28
  37. 42
  38. 6
  39. 8
  40. 120

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad