16 Choose 12
Combination Calculator
What is 16 choose 12?
Answer
16 choose 12 is
1,820
Order doesn't matter, no repeats: 1,820 ways to choose 12 of 16 items.
Choosing 12 of 16 is the same as leaving 4 out: C(16, 12) = C(16, 4).
C(16, 12) = 16! / (12! · 4!)
= C(16, 4)
= (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)
= 43,680 / 24
= 1,820
If order matters (permutations): P(16, 12) = 16 × 15 × 14 × … × 5 = 871,782,912,000 — each combination in 12! = 479,001,600 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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n choose 12 for other n
| n choose 12 | Answer |
|---|---|
| 12 choose 12 | 1 |
| 13 choose 12 | 13 |
| 14 choose 12 | 91 |
| 15 choose 12 | 455 |
| 16 choose 12 | 1,820 |
| 17 choose 12 | 6,188 |
| 18 choose 12 | 18,564 |
| 19 choose 12 | 50,388 |
| 20 choose 12 | 125,970 |