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

12 questions · Seed 104736 · 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(7, 5) — the number of ways to choose 5 items from 7 distinct items.
21
C(7, 5) = 7! ÷ (5! × 2!) = 21.
2. 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.
3. 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.
4. Evaluate the combination C(6, 3) — the number of ways to choose 3 items from 6 distinct items.
20
C(6, 3) = 6! ÷ (3! × 3!) = 20.
5. Evaluate the combination C(10, 5) — the number of ways to choose 5 items from 10 distinct items.
252
C(10, 5) = 10! ÷ (5! × 5!) = 252.
6. Evaluate the combination C(13, 3) — the number of ways to choose 3 items from 13 distinct items.
286
C(13, 3) = 13! ÷ (3! × 10!) = 286.
7. 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.
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(9, 4) — the number of ways to choose 4 items from 9 distinct items.
126
C(9, 4) = 9! ÷ (4! × 5!) = 126.
10. Evaluate the combination C(9, 2) — the number of ways to choose 2 items from 9 distinct items.
36
C(9, 2) = 9! ÷ (2! × 7!) = 36.
11. 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. 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.

12 questions · Seed 104736 · 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(7, 5) — the number of ways to choose 5 items from 7 distinct items.
7 · 5 · 5 · 7 · Unordered combinations C(n…
2. 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…
3. 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…
4. Evaluate the combination C(6, 3) — the number of ways to choose 3 items from 6 distinct items.
6 · 3 · 3 · 6 · Unordered combinations C(n…
5. Evaluate the combination C(10, 5) — the number of ways to choose 5 items from 10 distinct items.
10 · 5 · 5 · 10 · Unordered combinations C(n…
6. Evaluate the combination C(13, 3) — the number of ways to choose 3 items from 13 distinct items.
13 · 3 · 3 · 13 · Unordered combinations C(n…
7. 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…
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(9, 4) — the number of ways to choose 4 items from 9 distinct items.
9 · 4 · 4 · 9 · Unordered combinations C(n…
10. Evaluate the combination C(9, 2) — the number of ways to choose 2 items from 9 distinct items.
9 · 2 · 2 · 9 · Unordered combinations C(n…
11. 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. 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…

12 questions · Seed 104736 · 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(7, 5) — the number of ways to choose 5 items from 7 distinct items.
21
C(7, 5) = 7! ÷ (5! × 2!) = 21.
2. 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.
3. 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.
4. Evaluate the combination C(6, 3) — the number of ways to choose 3 items from 6 distinct items.
20
C(6, 3) = 6! ÷ (3! × 3!) = 20.
5. Evaluate the combination C(10, 5) — the number of ways to choose 5 items from 10 distinct items.
252
C(10, 5) = 10! ÷ (5! × 5!) = 252.
6. Evaluate the combination C(13, 3) — the number of ways to choose 3 items from 13 distinct items.
286
C(13, 3) = 13! ÷ (3! × 10!) = 286.
7. 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.
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(9, 4) — the number of ways to choose 4 items from 9 distinct items.
126
C(9, 4) = 9! ÷ (4! × 5!) = 126.
10. Evaluate the combination C(9, 2) — the number of ways to choose 2 items from 9 distinct items.
36
C(9, 2) = 9! ÷ (2! × 7!) = 36.
11. 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. 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.

12 questions · Seed 104736 · Age guidance, not curriculum certification