What is P(5, 2)? — 5 Permute 2
There are 20 possible permutations of 2 items chosen from 5 (nPr = 20), and 10 combinations (nCr = 10).
Exact Answer
P(5, 2) = 20
Combinations C(n,r)
10
Permutations P(n,r)
20
n! (5!)
120
r! (2!)
2
Step-by-Step Solution: P(5, 2) = 20
Step 1
Use the Permutations Formula nPr = n! / (n − r)!
Substitute n = 5 and r = 2: 5! = 120, (5−2)! = 6.
P(5, 2) = 20
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).