What is 5 Choose 3? — C(5, 3) Combinations
There are 10 possible combinations when choosing 3 items from 5 (nCr = 10), and 60 permutations (nPr = 60).
Exact Answer
C(5, 3) = 10
Combinations C(n,r)
10
Permutations P(n,r)
60
n! (5!)
120
r! (3!)
6
Step-by-Step Solution: C(5, 3) = 10
Step 1
Use the Combinations Formula nCr = n! / (r! × (n − r)!)
Substitute n = 5 and r = 3: 5! = 120, (5−3)! = 2, and 3! = 6.
C(5, 3) = 10
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 10 |
| Permutations P(n,r) | 60 |
| n! (5!) | 120 |
| r! (3!) | 6 |
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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).