What is 6 Choose 2? — C(6, 2) Combinations
There are 15 possible combinations when choosing 2 items from 6 (nCr = 15), and 30 permutations (nPr = 30).
Exact Answer
C(6, 2) = 15
Combinations C(n,r)
15
Permutations P(n,r)
30
n! (6!)
720
r! (2!)
2
Step-by-Step Solution: C(6, 2) = 15
Step 1
Use the Combinations Formula nCr = n! / (r! × (n − r)!)
Substitute n = 6 and r = 2: 6! = 720, (6−2)! = 24, and 2! = 2.
C(6, 2) = 15
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 15 |
| Permutations P(n,r) | 30 |
| n! (6!) | 720 |
| r! (2!) | 2 |
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Frequently Asked Questions
What is the difference between C(6,2) and P(6,2)?
Combinations C(6,2) = 15 (order does not matter), whereas Permutations P(6,2) = 30 (order matters).