What is 10 Choose 2? — C(10, 2) Combinations
There are 45 possible combinations when choosing 2 items from 10 (nCr = 45), and 90 permutations (nPr = 90).
Exact Answer
C(10, 2) = 45
Combinations C(n,r)
45
Permutations P(n,r)
90
n! (10!)
3,628,800
r! (2!)
2
Step-by-Step Solution: C(10, 2) = 45
Step 1
Use the Combinations Formula nCr = n! / (r! × (n − r)!)
Substitute n = 10 and r = 2: 10! = 3,628,800, (10−2)! = 40,320, and 2! = 2.
C(10, 2) = 45
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Combinations C(n,r) | 45 |
| Permutations P(n,r) | 90 |
| n! (10!) | 3,628,800 |
| r! (2!) | 2 |
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Frequently Asked Questions
What is the difference between C(10,2) and P(10,2)?
Combinations C(10,2) = 45 (order does not matter), whereas Permutations P(10,2) = 90 (order matters).