19 Choose 10
Combination Calculator
What is 19 choose 10?
Answer
19 choose 10 is
92,378
Order doesn't matter, no repeats: 92,378 ways to choose 10 of 19 items.
Choosing 10 of 19 is the same as leaving 9 out: C(19, 10) = C(19, 9).
C(19, 10) = 19! / (10! · 9!)
= C(19, 9)
= (19 × 18 × 17 × … × 11) / (9 × 8 × 7 × … × 1)
9 factors on top and bottom
= 33,522,128,640 / 362,880
= 92,378
If order matters (permutations): P(19, 10) = 19 × 18 × 17 × … × 10 = 335,221,286,400 — each combination in 10! = 3,628,800 orders.
| k | 19 choose k |
|---|---|
| 0 | 1 |
| 1 | 19 |
| 2 | 171 |
| 3 | 969 |
| 4 | 3,876 |
| 5 | 11,628 |
| 6 | 27,132 |
| 7 | 50,388 |
| 8 | 75,582 |
| 9 | 92,378 |
| 10 | 92,378 |
| 11 | 75,582 |
| 12 | 50,388 |
| 13 | 27,132 |
| 14 | 11,628 |
| 15 | 3,876 |
| 16 | 969 |
| 17 | 171 |
| 18 | 19 |
| 19 | 1 |
Row sum: 219 = 524,288 — all subsets of 19 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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