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