18 Choose 3
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What is 18 choose 3?
Answer
18 choose 3 is
816
Order doesn't matter, no repeats: 816 ways to choose 3 of 18 items.
C(18, 3) = 18! / (3! · 15!)
= (18 × 17 × 16) / (3 × 2 × 1)
= 4,896 / 6
= 816
If order matters (permutations): P(18, 3) = 18 × 17 × 16 = 4,896 — each combination in 3! = 6 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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