18 Choose 7
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What is 18 choose 7?
Answer
18 choose 7 is
31,824
Order doesn't matter, no repeats: 31,824 ways to choose 7 of 18 items.
C(18, 7) = 18! / (7! · 11!)
= (18 × 17 × 16 × … × 12) / (7 × 6 × 5 × … × 1)
7 factors on top and bottom
= 160,392,960 / 5,040
= 31,824
If order matters (permutations): P(18, 7) = 18 × 17 × 16 × … × 12 = 160,392,960 — each combination in 7! = 5,040 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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