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.

New variation Try interactive challenge Browse templates

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Unordered combinations C(n, r)

Take your time. Show your thinking.

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

12 questions · Seed 104731 · 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(6, 3) — the number of ways to choose 3 items from 6 distinct items.
20
C(6, 3) = 6! ÷ (3! × 3!) = 20.
2. 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.
3. Evaluate the combination C(11, 3) — the number of ways to choose 3 items from 11 distinct items.
165
C(11, 3) = 11! ÷ (3! × 8!) = 165.
4. 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.
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(10, 4) — the number of ways to choose 4 items from 10 distinct items.
210
C(10, 4) = 10! ÷ (4! × 6!) = 210.
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(11, 2) — the number of ways to choose 2 items from 11 distinct items.
55
C(11, 2) = 11! ÷ (2! × 9!) = 55.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 104731 · 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(6, 3) — the number of ways to choose 3 items from 6 distinct items.
6 · 3 · 3 · 6 · Unordered combinations C(n…
2. 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…
3. Evaluate the combination C(11, 3) — the number of ways to choose 3 items from 11 distinct items.
11 · 3 · 3 · 11 · Unordered combinations C(n…
4. 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…
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(10, 4) — the number of ways to choose 4 items from 10 distinct items.
10 · 4 · 4 · 10 · 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(11, 2) — the number of ways to choose 2 items from 11 distinct items.
11 · 2 · 2 · 11 · Unordered combinations C(n…
9. 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…
10. 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…
11. 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…
12. 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…

12 questions · Seed 104731 · 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(6, 3) — the number of ways to choose 3 items from 6 distinct items.
20
C(6, 3) = 6! ÷ (3! × 3!) = 20.
2. 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.
3. Evaluate the combination C(11, 3) — the number of ways to choose 3 items from 11 distinct items.
165
C(11, 3) = 11! ÷ (3! × 8!) = 165.
4. 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.
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(10, 4) — the number of ways to choose 4 items from 10 distinct items.
210
C(10, 4) = 10! ÷ (4! × 6!) = 210.
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(11, 2) — the number of ways to choose 2 items from 11 distinct items.
55
C(11, 2) = 11! ÷ (2! × 9!) = 55.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 104731 · Age guidance, not curriculum certification