ReasoningAges 16-18

Unordered combinations C(n, r)

Calculate unordered combinations C(n, r) when selecting a committee or subset without regard to order. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Unordered combinations C(n, r)

Take your time. Show your thinking.

1. Evaluate the combination C(5, 2) — the number of ways to choose 2 items from 5 distinct items.
5 · 2 · 2 · 5 · Unordered combinations C(n…
2. Evaluate the combination C(8, 4) — the number of ways to choose 4 items from 8 distinct items.
8 · 4 · 4 · 8 · Unordered combinations C(n…
3. Evaluate the combination C(9, 3) — the number of ways to choose 3 items from 9 distinct items.
9 · 3 · 3 · 9 · Unordered combinations C(n…
4. Evaluate the combination C(7, 2) — the number of ways to choose 2 items from 7 distinct items.
7 · 2 · 2 · 7 · Unordered combinations C(n…
5. Evaluate the combination C(4, 2) — the number of ways to choose 2 items from 4 distinct items.
4 · 2 · 2 · 4 · Unordered combinations C(n…
6. Evaluate the combination C(14, 4) — the number of ways to choose 4 items from 14 distinct items.
14 · 4 · 4 · 14 · Unordered combinations C(n…
7. Evaluate the combination C(7, 4) — the number of ways to choose 4 items from 7 distinct items.
7 · 4 · 4 · 7 · Unordered combinations C(n…
8. Evaluate the combination C(13, 4) — the number of ways to choose 4 items from 13 distinct items.
13 · 4 · 4 · 13 · Unordered combinations C(n…
9. Evaluate the combination C(10, 4) — the number of ways to choose 4 items from 10 distinct items.
10 · 4 · 4 · 10 · Unordered combinations C(n…
10. Evaluate the combination C(12, 2) — the number of ways to choose 2 items from 12 distinct items.
12 · 2 · 2 · 12 · Unordered combinations C(n…
11. Evaluate the combination C(10, 2) — the number of ways to choose 2 items from 10 distinct items.
10 · 2 · 2 · 10 · Unordered combinations C(n…
12. Evaluate the combination C(8, 2) — the number of ways to choose 2 items from 8 distinct items.
8 · 2 · 2 · 8 · Unordered combinations C(n…

12 questions · Seed 104734 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Unordered combinations C(n, r)

Answers and reasoning. Review before teaching.

1. Evaluate the combination C(5, 2) — the number of ways to choose 2 items from 5 distinct items.
10
C(5, 2) = 5! ÷ (2! × 3!) = 10.
2. Evaluate the combination C(8, 4) — the number of ways to choose 4 items from 8 distinct items.
70
C(8, 4) = 8! ÷ (4! × 4!) = 70.
3. Evaluate the combination C(9, 3) — the number of ways to choose 3 items from 9 distinct items.
84
C(9, 3) = 9! ÷ (3! × 6!) = 84.
4. Evaluate the combination C(7, 2) — the number of ways to choose 2 items from 7 distinct items.
21
C(7, 2) = 7! ÷ (2! × 5!) = 21.
5. Evaluate the combination C(4, 2) — the number of ways to choose 2 items from 4 distinct items.
6
C(4, 2) = 4! ÷ (2! × 2!) = 6.
6. Evaluate the combination C(14, 4) — the number of ways to choose 4 items from 14 distinct items.
1001
C(14, 4) = 14! ÷ (4! × 10!) = 1001.
7. Evaluate the combination C(7, 4) — the number of ways to choose 4 items from 7 distinct items.
35
C(7, 4) = 7! ÷ (4! × 3!) = 35.
8. Evaluate the combination C(13, 4) — the number of ways to choose 4 items from 13 distinct items.
715
C(13, 4) = 13! ÷ (4! × 9!) = 715.
9. Evaluate the combination C(10, 4) — the number of ways to choose 4 items from 10 distinct items.
210
C(10, 4) = 10! ÷ (4! × 6!) = 210.
10. Evaluate the combination C(12, 2) — the number of ways to choose 2 items from 12 distinct items.
66
C(12, 2) = 12! ÷ (2! × 10!) = 66.
11. Evaluate the combination C(10, 2) — the number of ways to choose 2 items from 10 distinct items.
45
C(10, 2) = 10! ÷ (2! × 8!) = 45.
12. Evaluate the combination C(8, 2) — the number of ways to choose 2 items from 8 distinct items.
28
C(8, 2) = 8! ÷ (2! × 6!) = 28.

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Unordered combinations C(n, r)

Take your time. Show your thinking.

1. Evaluate the combination C(5, 2) — the number of ways to choose 2 items from 5 distinct items.
5 · 2 · 2 · 5 · Unordered combinations C(n…
2. Evaluate the combination C(8, 4) — the number of ways to choose 4 items from 8 distinct items.
8 · 4 · 4 · 8 · Unordered combinations C(n…
3. Evaluate the combination C(9, 3) — the number of ways to choose 3 items from 9 distinct items.
9 · 3 · 3 · 9 · Unordered combinations C(n…
4. Evaluate the combination C(7, 2) — the number of ways to choose 2 items from 7 distinct items.
7 · 2 · 2 · 7 · Unordered combinations C(n…
5. Evaluate the combination C(4, 2) — the number of ways to choose 2 items from 4 distinct items.
4 · 2 · 2 · 4 · Unordered combinations C(n…
6. Evaluate the combination C(14, 4) — the number of ways to choose 4 items from 14 distinct items.
14 · 4 · 4 · 14 · Unordered combinations C(n…
7. Evaluate the combination C(7, 4) — the number of ways to choose 4 items from 7 distinct items.
7 · 4 · 4 · 7 · Unordered combinations C(n…
8. Evaluate the combination C(13, 4) — the number of ways to choose 4 items from 13 distinct items.
13 · 4 · 4 · 13 · Unordered combinations C(n…
9. Evaluate the combination C(10, 4) — the number of ways to choose 4 items from 10 distinct items.
10 · 4 · 4 · 10 · Unordered combinations C(n…
10. Evaluate the combination C(12, 2) — the number of ways to choose 2 items from 12 distinct items.
12 · 2 · 2 · 12 · Unordered combinations C(n…
11. Evaluate the combination C(10, 2) — the number of ways to choose 2 items from 10 distinct items.
10 · 2 · 2 · 10 · Unordered combinations C(n…
12. Evaluate the combination C(8, 2) — the number of ways to choose 2 items from 8 distinct items.
8 · 2 · 2 · 8 · Unordered combinations C(n…

12 questions · Seed 104734 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Unordered combinations C(n, r)

Answers and reasoning. Review before teaching.

1. Evaluate the combination C(5, 2) — the number of ways to choose 2 items from 5 distinct items.
10
C(5, 2) = 5! ÷ (2! × 3!) = 10.
2. Evaluate the combination C(8, 4) — the number of ways to choose 4 items from 8 distinct items.
70
C(8, 4) = 8! ÷ (4! × 4!) = 70.
3. Evaluate the combination C(9, 3) — the number of ways to choose 3 items from 9 distinct items.
84
C(9, 3) = 9! ÷ (3! × 6!) = 84.
4. Evaluate the combination C(7, 2) — the number of ways to choose 2 items from 7 distinct items.
21
C(7, 2) = 7! ÷ (2! × 5!) = 21.
5. Evaluate the combination C(4, 2) — the number of ways to choose 2 items from 4 distinct items.
6
C(4, 2) = 4! ÷ (2! × 2!) = 6.
6. Evaluate the combination C(14, 4) — the number of ways to choose 4 items from 14 distinct items.
1001
C(14, 4) = 14! ÷ (4! × 10!) = 1001.
7. Evaluate the combination C(7, 4) — the number of ways to choose 4 items from 7 distinct items.
35
C(7, 4) = 7! ÷ (4! × 3!) = 35.
8. Evaluate the combination C(13, 4) — the number of ways to choose 4 items from 13 distinct items.
715
C(13, 4) = 13! ÷ (4! × 9!) = 715.
9. Evaluate the combination C(10, 4) — the number of ways to choose 4 items from 10 distinct items.
210
C(10, 4) = 10! ÷ (4! × 6!) = 210.
10. Evaluate the combination C(12, 2) — the number of ways to choose 2 items from 12 distinct items.
66
C(12, 2) = 12! ÷ (2! × 10!) = 66.
11. Evaluate the combination C(10, 2) — the number of ways to choose 2 items from 10 distinct items.
45
C(10, 2) = 10! ÷ (2! × 8!) = 45.
12. Evaluate the combination C(8, 2) — the number of ways to choose 2 items from 8 distinct items.
28
C(8, 2) = 8! ÷ (2! × 6!) = 28.

12 questions · Seed 104734 · Age guidance, not curriculum certification