What is 5 Choose 2? — C(5, 2) Combinations
There are 10 possible combinations when choosing 2 items from 5 (nCr = 10), and 20 permutations (nPr = 20).
Exact Answer
C(5, 2) = 10
Combinations C(n,r)
10
Permutations P(n,r)
20
n! (5!)
120
r! (2!)
2
Step-by-Step Solution: C(5, 2) = 10
Step 1
Use the Combinations Formula nCr = n! / (r! × (n − r)!)
Substitute n = 5 and r = 2: 5! = 120, (5−2)! = 6, and 2! = 2.
C(5, 2) = 10
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 10 |
| Permutations P(n,r) | 20 |
| n! (5!) | 120 |
| r! (2!) | 2 |
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Frequently Asked Questions
What is the difference between C(5,2) and P(5,2)?
Combinations C(5,2) = 10 (order does not matter), whereas Permutations P(5,2) = 20 (order matters).