15 Choose 3
Combination Calculator
What is 15 choose 3?
Answer
15 choose 3 is
455
Order doesn't matter, no repeats: 455 ways to choose 3 of 15 items.
C(15, 3) = 15! / (3! · 12!)
= (15 × 14 × 13) / (3 × 2 × 1)
= 2,730 / 6
= 455
If order matters (permutations): P(15, 3) = 15 × 14 × 13 = 2,730 — each combination in 3! = 6 orders.
| k | 15 choose k |
|---|---|
| 0 | 1 |
| 1 | 15 |
| 2 | 105 |
| 3 | 455 |
| 4 | 1,365 |
| 5 | 3,003 |
| 6 | 5,005 |
| 7 | 6,435 |
| 8 | 6,435 |
| 9 | 5,005 |
| 10 | 3,003 |
| 11 | 1,365 |
| 12 | 455 |
| 13 | 105 |
| 14 | 15 |
| 15 | 1 |
Row sum: 215 = 32,768 — all subsets of 15 items.
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See Also
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