16 Choose 9
Combination Calculator
What is 16 choose 9?
Answer
16 choose 9 is
11,440
Order doesn't matter, no repeats: 11,440 ways to choose 9 of 16 items.
Choosing 9 of 16 is the same as leaving 7 out: C(16, 9) = C(16, 7).
C(16, 9) = 16! / (9! · 7!)
= C(16, 7)
= (16 × 15 × 14 × … × 10) / (7 × 6 × 5 × … × 1)
7 factors on top and bottom
= 57,657,600 / 5,040
= 11,440
If order matters (permutations): P(16, 9) = 16 × 15 × 14 × … × 8 = 4,151,347,200 — each combination in 9! = 362,880 orders.
| k | 16 choose k |
|---|---|
| 0 | 1 |
| 1 | 16 |
| 2 | 120 |
| 3 | 560 |
| 4 | 1,820 |
| 5 | 4,368 |
| 6 | 8,008 |
| 7 | 11,440 |
| 8 | 12,870 |
| 9 | 11,440 |
| 10 | 8,008 |
| 11 | 4,368 |
| 12 | 1,820 |
| 13 | 560 |
| 14 | 120 |
| 15 | 16 |
| 16 | 1 |
Row sum: 216 = 65,536 — all subsets of 16 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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