4 Choose 2 = 6
There are 6 ways to choose 2 items from 4 when order does not matter. It is the smallest useful worked example of n choose r: the unordered pairs in a set of 4.
Combinations (4C2)
6
Permutations (4P2)
12
How 4 choose 2 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 4 and r = 2 gives:
C(4, 2) = 4! / (2! × 2!)
= 12 / 2
= 6The 2! in the denominator cancels all but the top 2 factors of 4!, so 4 choose 2 is the product of 2 descending terms starting at 4, divided by 2!. That product, 12, is the number of ordered arrangements (4P2); dividing by 2! = 2 removes the duplicate orderings and leaves 6.
Calculate other values
Need a different n and r? The full calculator handles any values, including permutations, and gives you a shareable link for the result.
Open the n choose r calculator