Answers Binomial Coefficient Calculator

What is 21C6?

This is a binomial coefficient question. 21C6 means choosing 6 items from 21 distinct items without repetition and without regard to order.

Exact result

54,264

The binomial coefficient C(21, 6) is 54,264.

21C6 counts unordered groups of 6 drawn from 21 distinct items. It is the same value as 21 choose 6.

Worked steps

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  1. Inputs: n = 21, r = 6
  2. Formula: C(n, r) = nCr = n! / r!(n - r)!
  3. Substitute: C(21, 6) = 21! / (6!(21-6)!)
  4. Steps: 51,090,942,171,709,440,000 / (720 x 1,307,674,368,000)
  5. Result: The binomial coefficient C(21, 6) is 54,264.

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21C6 counts unordered groups of 6 drawn from 21 distinct items. It is the same value as 21 choose 6.

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