18 Choose 10
Combination Calculator
What is 18 choose 10?
Answer
18 choose 10 is
43,758
Order doesn't matter, no repeats: 43,758 ways to choose 10 of 18 items.
Choosing 10 of 18 is the same as leaving 8 out: C(18, 10) = C(18, 8).
C(18, 10) = 18! / (10! · 8!)
= C(18, 8)
= (18 × 17 × 16 × … × 11) / (8 × 7 × 6 × … × 1)
8 factors on top and bottom
= 1,764,322,560 / 40,320
= 43,758
If order matters (permutations): P(18, 10) = 18 × 17 × 16 × … × 9 = 158,789,030,400 — each combination in 10! = 3,628,800 orders.
| k | 18 choose k |
|---|---|
| 0 | 1 |
| 1 | 18 |
| 2 | 153 |
| 3 | 816 |
| 4 | 3,060 |
| 5 | 8,568 |
| 6 | 18,564 |
| 7 | 31,824 |
| 8 | 43,758 |
| 9 | 48,620 |
| 10 | 43,758 |
| 11 | 31,824 |
| 12 | 18,564 |
| 13 | 8,568 |
| 14 | 3,060 |
| 15 | 816 |
| 16 | 153 |
| 17 | 18 |
| 18 | 1 |
Row sum: 218 = 262,144 — all subsets of 18 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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