7 Choose 3 = 35
There are 35 ways to choose 3 items from 7 when order does not matter. It answers questions like how many different 3-person subgroups a group of 7 can form.
Combinations (7C3)
35
Permutations (7P3)
210
How 7 choose 3 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 7 and r = 3 gives:
C(7, 3) = 7! / (3! × 4!)
= 210 / 6
= 35The 4! in the denominator cancels all but the top 3 factors of 7!, so 7 choose 3 is the product of 3 descending terms starting at 7, divided by 3!. That product, 210, is the number of ordered arrangements (7P3); dividing by 3! = 6 removes the duplicate orderings and leaves 35.
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