18 Choose 9
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What is 18 choose 9?
Answer
18 choose 9 is
48,620
Order doesn't matter, no repeats: 48,620 ways to choose 9 of 18 items.
C(18, 9) = 18! / (9! · 9!)
= (18 × 17 × 16 × … × 10) / (9 × 8 × 7 × … × 1)
9 factors on top and bottom
= 17,643,225,600 / 362,880
= 48,620
If order matters (permutations): P(18, 9) = 18 × 17 × 16 × … × 10 = 17,643,225,600 — each combination in 9! = 362,880 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
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