What is 8 Choose 3? — C(8, 3) Combinations
There are 56 possible combinations when choosing 3 items from 8 (nCr = 56), and 336 permutations (nPr = 336).
Exact Answer
C(8, 3) = 56
Combinations C(n,r)
56
Permutations P(n,r)
336
n! (8!)
40,320
r! (3!)
6
Step-by-Step Solution: C(8, 3) = 56
Step 1
Use the Combinations Formula nCr = n! / (r! × (n − r)!)
Substitute n = 8 and r = 3: 8! = 40,320, (8−3)! = 120, and 3! = 6.
C(8, 3) = 56
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 56 |
| Permutations P(n,r) | 336 |
| n! (8!) | 40,320 |
| r! (3!) | 6 |
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Frequently Asked Questions
What is the difference between C(8,3) and P(8,3)?
Combinations C(8,3) = 56 (order does not matter), whereas Permutations P(8,3) = 336 (order matters).