17 Choose 9
Combination Calculator
What is 17 choose 9?
Answer
17 choose 9 is
24,310
Order doesn't matter, no repeats: 24,310 ways to choose 9 of 17 items.
Choosing 9 of 17 is the same as leaving 8 out: C(17, 9) = C(17, 8).
C(17, 9) = 17! / (9! · 8!)
= C(17, 8)
= (17 × 16 × 15 × … × 10) / (8 × 7 × 6 × … × 1)
8 factors on top and bottom
= 980,179,200 / 40,320
= 24,310
If order matters (permutations): P(17, 9) = 17 × 16 × 15 × … × 9 = 8,821,612,800 — each combination in 9! = 362,880 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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