Answers Binomial Coefficient Calculator

What is 10C3?

This is a binomial coefficient question. 10C3 is notation for a combination without repetition, so you are choosing 3 items from 10 distinct items and order does not matter.

Exact result

120

The binomial coefficient C(10, 3) is 120.

10C3 counts unordered groups of 3 drawn from 10 distinct items. It is the same value as 10 choose 3.

Worked steps

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  1. Inputs: n = 10, r = 3
  2. Formula: C(n, r) = nCr = n! / r!(n - r)!
  3. Substitute: C(10, 3) = 10! / (3!(10-3)!)
  4. Steps: 3,628,800 / (6 x 5,040)
  5. Result: The binomial coefficient C(10, 3) is 120.

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10C3 counts unordered groups of 3 drawn from 10 distinct items. It is the same value as 10 choose 3.

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