15 Choose 10
Combination Calculator
What is 15 choose 10?
Answer
15 choose 10 is
3,003
Order doesn't matter, no repeats: 3,003 ways to choose 10 of 15 items.
Choosing 10 of 15 is the same as leaving 5 out: C(15, 10) = C(15, 5).
C(15, 10) = 15! / (10! · 5!)
= C(15, 5)
= (15 × 14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)
= 360,360 / 120
= 3,003
If order matters (permutations): P(15, 10) = 15 × 14 × 13 × … × 6 = 10,897,286,400 — each combination in 10! = 3,628,800 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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