22 Combinations of 3
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2 min read
Evaluate the combination:
22C3
A unique order or arrangement
| nCr = | n! |
| r!(n - r)! |
where n is the number of items
r is the unique arrangements.
| 22C3 2 | 22! |
| 3!(22 - 3)! |
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
n! = 22!
22! = 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
22! = 1,124,000,727,777,607,680,000
(n - r)! = (22 - 3)!
(22 - 3)! = 19!
19! = 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
19! = 121,645,100,408,832,000
r! = 3!
3! = 3 x 2 x 1
3! = 6
| 22C3 = | 1,124,000,727,777,607,680,000 |
| 6 x 121,645,100,408,832,000 |
| 22C3 = | 1,124,000,727,777,607,680,000 |
| 729,870,602,452,992,000 |
22C3 = 1,540
