15 Choose 7
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What is 15 choose 7?
Answer
15 choose 7 is
6,435
Order doesn't matter, no repeats: 6,435 ways to choose 7 of 15 items.
C(15, 7) = 15! / (7! · 8!)
= (15 × 14 × 13 × … × 9) / (7 × 6 × 5 × … × 1)
7 factors on top and bottom
= 32,432,400 / 5,040
= 6,435
If order matters (permutations): P(15, 7) = 15 × 14 × 13 × … × 9 = 32,432,400 — each combination in 7! = 5,040 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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- Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
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