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

12 questions · Seed 42 · 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, 3) — the number of ways to choose 3 items from 5 distinct items.
10
C(5, 3) = 5! ÷ (3! × 2!) = 10.
2. Evaluate the combination C(11, 4) — the number of ways to choose 4 items from 11 distinct items.
330
C(11, 4) = 11! ÷ (4! × 7!) = 330.
3. 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.
4. 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.
5. Evaluate the combination C(13, 5) — the number of ways to choose 5 items from 13 distinct items.
1287
C(13, 5) = 13! ÷ (5! × 8!) = 1287.
6. Evaluate the combination C(8, 5) — the number of ways to choose 5 items from 8 distinct items.
56
C(8, 5) = 8! ÷ (5! × 3!) = 56.
7. 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.
8. Evaluate the combination C(8, 3) — the number of ways to choose 3 items from 8 distinct items.
56
C(8, 3) = 8! ÷ (3! × 5!) = 56.
9. Evaluate the combination C(6, 2) — the number of ways to choose 2 items from 6 distinct items.
15
C(6, 2) = 6! ÷ (2! × 4!) = 15.
10. 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.
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(10, 2) — the number of ways to choose 2 items from 10 distinct items.
45
C(10, 2) = 10! ÷ (2! × 8!) = 45.

12 questions · Seed 42 · 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, 3) — the number of ways to choose 3 items from 5 distinct items.
5 · 3 · 3 · 5 · Unordered combinations C(n…
2. Evaluate the combination C(11, 4) — the number of ways to choose 4 items from 11 distinct items.
11 · 4 · 4 · 11 · Unordered combinations C(n…
3. 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…
4. 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…
5. Evaluate the combination C(13, 5) — the number of ways to choose 5 items from 13 distinct items.
13 · 5 · 5 · 13 · Unordered combinations C(n…
6. Evaluate the combination C(8, 5) — the number of ways to choose 5 items from 8 distinct items.
8 · 5 · 5 · 8 · Unordered combinations C(n…
7. 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…
8. Evaluate the combination C(8, 3) — the number of ways to choose 3 items from 8 distinct items.
8 · 3 · 3 · 8 · Unordered combinations C(n…
9. Evaluate the combination C(6, 2) — the number of ways to choose 2 items from 6 distinct items.
6 · 2 · 2 · 6 · Unordered combinations C(n…
10. 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…
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(10, 2) — the number of ways to choose 2 items from 10 distinct items.
10 · 2 · 2 · 10 · Unordered combinations C(n…

12 questions · Seed 42 · 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, 3) — the number of ways to choose 3 items from 5 distinct items.
10
C(5, 3) = 5! ÷ (3! × 2!) = 10.
2. Evaluate the combination C(11, 4) — the number of ways to choose 4 items from 11 distinct items.
330
C(11, 4) = 11! ÷ (4! × 7!) = 330.
3. 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.
4. 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.
5. Evaluate the combination C(13, 5) — the number of ways to choose 5 items from 13 distinct items.
1287
C(13, 5) = 13! ÷ (5! × 8!) = 1287.
6. Evaluate the combination C(8, 5) — the number of ways to choose 5 items from 8 distinct items.
56
C(8, 5) = 8! ÷ (5! × 3!) = 56.
7. 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.
8. Evaluate the combination C(8, 3) — the number of ways to choose 3 items from 8 distinct items.
56
C(8, 3) = 8! ÷ (3! × 5!) = 56.
9. Evaluate the combination C(6, 2) — the number of ways to choose 2 items from 6 distinct items.
15
C(6, 2) = 6! ÷ (2! × 4!) = 15.
10. 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.
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(10, 2) — the number of ways to choose 2 items from 10 distinct items.
45
C(10, 2) = 10! ÷ (2! × 8!) = 45.

12 questions · Seed 42 · Age guidance, not curriculum certification