14 Choose 10
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What is 14 choose 10?
Answer
14 choose 10 is
1,001
Order doesn't matter, no repeats: 1,001 ways to choose 10 of 14 items.
Choosing 10 of 14 is the same as leaving 4 out: C(14, 10) = C(14, 4).
C(14, 10) = 14! / (10! · 4!)
= C(14, 4)
= (14 × 13 × 12 × 11) / (4 × 3 × 2 × 1)
= 24,024 / 24
= 1,001
If order matters (permutations): P(14, 10) = 14 × 13 × 12 × … × 5 = 3,632,428,800 — each combination in 10! = 3,628,800 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
- Random Number Generator - Pick a random whole number between two bounds
- Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
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