15 Choose 9
Combination Calculator
What is 15 choose 9?
Answer
15 choose 9 is
5,005
Order doesn't matter, no repeats: 5,005 ways to choose 9 of 15 items.
Choosing 9 of 15 is the same as leaving 6 out: C(15, 9) = C(15, 6).
C(15, 9) = 15! / (9! · 6!)
= C(15, 6)
= (15 × 14 × 13 × 12 × 11 × 10) / (6 × 5 × 4 × 3 × 2 × 1)
= 3,603,600 / 720
= 5,005
If order matters (permutations): P(15, 9) = 15 × 14 × 13 × … × 7 = 1,816,214,400 — each combination in 9! = 362,880 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
- Random Number Generator - Pick a random whole number between two bounds
- Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
- Factors of a Number - List all Factors and Factor Pairs of a Number
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