What is P(5, 3)? — 5 Permute 3
There are 60 possible permutations of 3 items chosen from 5 (nPr = 60), and 10 combinations (nCr = 10).
Exact Answer
P(5, 3) = 60
Combinations C(n,r)
10
Permutations P(n,r)
60
n! (5!)
120
r! (3!)
6
Step-by-Step Solution: P(5, 3) = 60
Step 1
Use the Permutations Formula nPr = n! / (n − r)!
Substitute n = 5 and r = 3: 5! = 120, (5−3)! = 2.
P(5, 3) = 60
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 10 |
| Permutations P(n,r) | 60 |
| n! (5!) | 120 |
| r! (3!) | 6 |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is the difference between C(5,3) and P(5,3)?
Combinations C(5,3) = 10 (order does not matter), whereas Permutations P(5,3) = 60 (order matters).