14 Choose 3
Combination Calculator
What is 14 choose 3?
Answer
14 choose 3 is
364
Order doesn't matter, no repeats: 364 ways to choose 3 of 14 items.
C(14, 3) = 14! / (3! · 11!)
= (14 × 13 × 12) / (3 × 2 × 1)
= 2,184 / 6
= 364
If order matters (permutations): P(14, 3) = 14 × 13 × 12 = 2,184 — each combination in 3! = 6 orders.
| k | 14 choose k |
|---|---|
| 0 | 1 |
| 1 | 14 |
| 2 | 91 |
| 3 | 364 |
| 4 | 1,001 |
| 5 | 2,002 |
| 6 | 3,003 |
| 7 | 3,432 |
| 8 | 3,003 |
| 9 | 2,002 |
| 10 | 1,001 |
| 11 | 364 |
| 12 | 91 |
| 13 | 14 |
| 14 | 1 |
Row sum: 214 = 16,384 — all subsets of 14 items.
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See Also
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