17 Choose 11
Combination Calculator
What is 17 choose 11?
Answer
17 choose 11 is
12,376
Order doesn't matter, no repeats: 12,376 ways to choose 11 of 17 items.
Choosing 11 of 17 is the same as leaving 6 out: C(17, 11) = C(17, 6).
C(17, 11) = 17! / (11! · 6!)
= C(17, 6)
= (17 × 16 × 15 × 14 × 13 × 12) / (6 × 5 × 4 × 3 × 2 × 1)
= 8,910,720 / 720
= 12,376
If order matters (permutations): P(17, 11) = 17 × 16 × 15 × … × 7 = 494,010,316,800 — each combination in 11! = 39,916,800 orders.
| k | 17 choose k |
|---|---|
| 0 | 1 |
| 1 | 17 |
| 2 | 136 |
| 3 | 680 |
| 4 | 2,380 |
| 5 | 6,188 |
| 6 | 12,376 |
| 7 | 19,448 |
| 8 | 24,310 |
| 9 | 24,310 |
| 10 | 19,448 |
| 11 | 12,376 |
| 12 | 6,188 |
| 13 | 2,380 |
| 14 | 680 |
| 15 | 136 |
| 16 | 17 |
| 17 | 1 |
Row sum: 217 = 131,072 — all subsets of 17 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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