What is P(6, 3)? — 6 Permute 3
There are 120 possible permutations of 3 items chosen from 6 (nPr = 120), and 20 combinations (nCr = 20).
Exact Answer
P(6, 3) = 120
Combinations C(n,r)
20
Permutations P(n,r)
120
n! (6!)
720
r! (3!)
6
Step-by-Step Solution: P(6, 3) = 120
Step 1
Use the Permutations Formula nPr = n! / (n − r)!
Substitute n = 6 and r = 3: 6! = 720, (6−3)! = 6.
P(6, 3) = 120
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 20 |
| Permutations P(n,r) | 120 |
| n! (6!) | 720 |
| r! (3!) | 6 |
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Frequently Asked Questions
What is the difference between C(6,3) and P(6,3)?
Combinations C(6,3) = 20 (order does not matter), whereas Permutations P(6,3) = 120 (order matters).