What is P(10, 2)? — 10 Permute 2
There are 90 possible permutations of 2 items chosen from 10 (nPr = 90), and 45 combinations (nCr = 45).
Exact Answer
P(10, 2) = 90
Combinations C(n,r)
45
Permutations P(n,r)
90
n! (10!)
3,628,800
r! (2!)
2
Step-by-Step Solution: P(10, 2) = 90
Step 1
Use the Permutations Formula nPr = n! / (n − r)!
Substitute n = 10 and r = 2: 10! = 3,628,800, (10−2)! = 40,320.
P(10, 2) = 90
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 45 |
| Permutations P(n,r) | 90 |
| n! (10!) | 3,628,800 |
| r! (2!) | 2 |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is the difference between C(10,2) and P(10,2)?
Combinations C(10,2) = 45 (order does not matter), whereas Permutations P(10,2) = 90 (order matters).