14 Choose 11
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What is 14 choose 11?
Answer
14 choose 11 is
364
Order doesn't matter, no repeats: 364 ways to choose 11 of 14 items.
Choosing 11 of 14 is the same as leaving 3 out: C(14, 11) = C(14, 3).
C(14, 11) = 14! / (11! · 3!)
= C(14, 3)
= (14 × 13 × 12) / (3 × 2 × 1)
= 2,184 / 6
= 364
If order matters (permutations): P(14, 11) = 14 × 13 × 12 × … × 4 = 14,529,715,200 — each combination in 11! = 39,916,800 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
- Factors of a Number - List all Factors and Factor Pairs of a Number
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