10 Choose 3 = 120
There are 120 ways to choose 3 items from 10 when order does not matter. It is the standard classroom example: forming a 3-person committee from 10 students.
Combinations (10C3)
120
Permutations (10P3)
720
How 10 choose 3 is calculated
The combinations formula is C(n, r) = n! / (r! × (n − r)!). Substituting n = 10 and r = 3 gives:
C(10, 3) = 10! / (3! × 7!)
= 720 / 6
= 120The 7! in the denominator cancels all but the top 3 factors of 10!, so 10 choose 3 is the product of 3 descending terms starting at 10, divided by 3!. That product, 720, is the number of ordered arrangements (10P3); dividing by 3! = 6 removes the duplicate orderings and leaves 120.
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