What is P(10, 3)? — 10 Permute 3
There are 720 possible permutations of 3 items chosen from 10 (nPr = 720), and 120 combinations (nCr = 120).
Exact Answer
P(10, 3) = 720
Combinations C(n,r)
120
Permutations P(n,r)
720
n! (10!)
3,628,800
r! (3!)
6
Step-by-Step Solution: P(10, 3) = 720
Step 1
Use the Permutations Formula nPr = n! / (n − r)!
Substitute n = 10 and r = 3: 10! = 3,628,800, (10−3)! = 5,040.
P(10, 3) = 720
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 120 |
| Permutations P(n,r) | 720 |
| n! (10!) | 3,628,800 |
| 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(10,3) and P(10,3)?
Combinations C(10,3) = 120 (order does not matter), whereas Permutations P(10,3) = 720 (order matters).