What is 12 Choose 4? — C(12, 4) Combinations
There are 495 possible combinations when choosing 4 items from 12 (nCr = 495), and 11880 permutations (nPr = 11880).
Exact Answer
C(12, 4) = 495
Combinations C(n,r)
495
Permutations P(n,r)
11,880
n! (12!)
479,001,600
r! (4!)
24
Step-by-Step Solution: C(12, 4) = 495
Step 1
Use the Combinations Formula nCr = n! / (r! × (n − r)!)
Substitute n = 12 and r = 4: 12! = 479,001,600, (12−4)! = 40,320, and 4! = 24.
C(12, 4) = 495
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 495 |
| Permutations P(n,r) | 11,880 |
| n! (12!) | 479,001,600 |
| r! (4!) | 24 |
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Frequently Asked Questions
What is the difference between C(12,4) and P(12,4)?
Combinations C(12,4) = 495 (order does not matter), whereas Permutations P(12,4) = 11880 (order matters).