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(13, 3) — the number of ways to choose 3 items from 13 distinct items.
13 · 3 · 3 · 13 · Unordered combinations C(n…
2. 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…
3. 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…
4. Evaluate the combination C(12, 4) — the number of ways to choose 4 items from 12 distinct items.
12 · 4 · 4 · 12 · Unordered combinations C(n…
5. Evaluate the combination C(11, 5) — the number of ways to choose 5 items from 11 distinct items.
11 · 5 · 5 · 11 · 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(6, 4) — the number of ways to choose 4 items from 6 distinct items.
6 · 4 · 4 · 6 · Unordered combinations C(n…
8. 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…
9. Evaluate the combination C(15, 5) — the number of ways to choose 5 items from 15 distinct items.
15 · 5 · 5 · 15 · Unordered combinations C(n…
10. 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…
11. Evaluate the combination C(9, 5) — the number of ways to choose 5 items from 9 distinct items.
9 · 5 · 5 · 9 · 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 104735 · 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(13, 3) — the number of ways to choose 3 items from 13 distinct items.
286
C(13, 3) = 13! ÷ (3! × 10!) = 286.
2. 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.
3. 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.
4. Evaluate the combination C(12, 4) — the number of ways to choose 4 items from 12 distinct items.
495
C(12, 4) = 12! ÷ (4! × 8!) = 495.
5. Evaluate the combination C(11, 5) — the number of ways to choose 5 items from 11 distinct items.
462
C(11, 5) = 11! ÷ (5! × 6!) = 462.
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(6, 4) — the number of ways to choose 4 items from 6 distinct items.
15
C(6, 4) = 6! ÷ (4! × 2!) = 15.
8. 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.
9. Evaluate the combination C(15, 5) — the number of ways to choose 5 items from 15 distinct items.
3003
C(15, 5) = 15! ÷ (5! × 10!) = 3003.
10. 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.
11. Evaluate the combination C(9, 5) — the number of ways to choose 5 items from 9 distinct items.
126
C(9, 5) = 9! ÷ (5! × 4!) = 126.
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 104735 · 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(13, 3) — the number of ways to choose 3 items from 13 distinct items.
13 · 3 · 3 · 13 · Unordered combinations C(n…
2. 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…
3. 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…
4. Evaluate the combination C(12, 4) — the number of ways to choose 4 items from 12 distinct items.
12 · 4 · 4 · 12 · Unordered combinations C(n…
5. Evaluate the combination C(11, 5) — the number of ways to choose 5 items from 11 distinct items.
11 · 5 · 5 · 11 · 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(6, 4) — the number of ways to choose 4 items from 6 distinct items.
6 · 4 · 4 · 6 · Unordered combinations C(n…
8. 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…
9. Evaluate the combination C(15, 5) — the number of ways to choose 5 items from 15 distinct items.
15 · 5 · 5 · 15 · Unordered combinations C(n…
10. 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…
11. Evaluate the combination C(9, 5) — the number of ways to choose 5 items from 9 distinct items.
9 · 5 · 5 · 9 · 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 104735 · 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(13, 3) — the number of ways to choose 3 items from 13 distinct items.
286
C(13, 3) = 13! ÷ (3! × 10!) = 286.
2. 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.
3. 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.
4. Evaluate the combination C(12, 4) — the number of ways to choose 4 items from 12 distinct items.
495
C(12, 4) = 12! ÷ (4! × 8!) = 495.
5. Evaluate the combination C(11, 5) — the number of ways to choose 5 items from 11 distinct items.
462
C(11, 5) = 11! ÷ (5! × 6!) = 462.
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(6, 4) — the number of ways to choose 4 items from 6 distinct items.
15
C(6, 4) = 6! ÷ (4! × 2!) = 15.
8. 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.
9. Evaluate the combination C(15, 5) — the number of ways to choose 5 items from 15 distinct items.
3003
C(15, 5) = 15! ÷ (5! × 10!) = 3003.
10. 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.
11. Evaluate the combination C(9, 5) — the number of ways to choose 5 items from 9 distinct items.
126
C(9, 5) = 9! ÷ (5! × 4!) = 126.
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 104735 · Age guidance, not curriculum certification