14 Choose 9
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What is 14 choose 9?
Answer
14 choose 9 is
2,002
Order doesn't matter, no repeats: 2,002 ways to choose 9 of 14 items.
Choosing 9 of 14 is the same as leaving 5 out: C(14, 9) = C(14, 5).
C(14, 9) = 14! / (9! · 5!)
= C(14, 5)
= (14 × 13 × 12 × 11 × 10) / (5 × 4 × 3 × 2 × 1)
= 240,240 / 120
= 2,002
If order matters (permutations): P(14, 9) = 14 × 13 × 12 × … × 6 = 726,485,760 — each combination in 9! = 362,880 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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