16 Choose 10
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What is 16 choose 10?
Answer
16 choose 10 is
8,008
Order doesn't matter, no repeats: 8,008 ways to choose 10 of 16 items.
Choosing 10 of 16 is the same as leaving 6 out: C(16, 10) = C(16, 6).
C(16, 10) = 16! / (10! · 6!)
= C(16, 6)
= (16 × 15 × 14 × 13 × 12 × 11) / (6 × 5 × 4 × 3 × 2 × 1)
= 5,765,760 / 720
= 8,008
If order matters (permutations): P(16, 10) = 16 × 15 × 14 × … × 7 = 29,059,430,400 — each combination in 10! = 3,628,800 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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