17 Choose 10
Combination Calculator
What is 17 choose 10?
Answer
17 choose 10 is
19,448
Order doesn't matter, no repeats: 19,448 ways to choose 10 of 17 items.
Choosing 10 of 17 is the same as leaving 7 out: C(17, 10) = C(17, 7).
C(17, 10) = 17! / (10! · 7!)
= C(17, 7)
= (17 × 16 × 15 × … × 11) / (7 × 6 × 5 × … × 1)
7 factors on top and bottom
= 98,017,920 / 5,040
= 19,448
If order matters (permutations): P(17, 10) = 17 × 16 × 15 × … × 8 = 70,572,902,400 — each combination in 10! = 3,628,800 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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