Worked example
A group of 2 people is chosen from 5 people. Order does not matter. How many different groups are possible?
Answer & why
Answer: 10
Use combinations: 5! / (2! × 3!) = 10. Each unordered group is counted once.
Grade 11 · Math
Count unordered selections
Count selections where order does not matter.
8 authored questions + worked example
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All questions
All 8 authored questions for this skill.
Question 1
A group of 3 people is chosen from 9 people. Order does not matter. How many different groups are possible?
- 85
- 86
- 83
- 84
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 84
Use combinations: 9! / (3! × 6!) = 84. Each unordered group is counted once.
Question 2
A group of 3 people is chosen from 10 people. Order does not matter. How many different groups are possible?
- 122
- 119
- 120
- 121
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 120
Use combinations: 10! / (3! × 7!) = 120. Each unordered group is counted once.
Question 3
A group of 2 people is chosen from 5 people. Order does not matter. How many different groups are possible?
- 9
- 11
- 12
- 10
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 10
Use combinations: 5! / (2! × 3!) = 10. Each unordered group is counted once.
Question 4
A group of 2 people is chosen from 6 people. Order does not matter. How many different groups are possible?
- 17
- 16
- 14
- 15
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 15
Use combinations: 6! / (2! × 4!) = 15. Each unordered group is counted once.
Question 5
A group of 3 people is chosen from 7 people. Order does not matter. How many different groups are possible?
- 37
- 35
- 34
- 36
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 35
Use combinations: 7! / (3! × 4!) = 35. Each unordered group is counted once.
Question 6
A group of 2 people is chosen from 8 people. Order does not matter. How many different groups are possible?
- 30
- 29
- 27
- 28
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 28
Use combinations: 8! / (2! × 6!) = 28. Each unordered group is counted once.
Question 7
A group of 3 people is chosen from 8 people. Order does not matter. How many different groups are possible?
- 57
- 58
- 56
- 55
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 56
Use combinations: 8! / (3! × 5!) = 56. Each unordered group is counted once.
Question 8
A group of 2 people is chosen from 9 people. Order does not matter. How many different groups are possible?
- 36
- 38
- 35
- 37
A hint
Use combinations when changing the order does not create a new group.
Answer & why
Answer: 36
Use combinations: 9! / (2! × 7!) = 36. Each unordered group is counted once.