Multinomial Coefficient Calculator (with Examples)

The multinomial calculator allows us to calculate the coefficients that occur in the multinomial expansion of a polynomial. It is calculated using the formula,

How to find Multinomial Coefficient – Example Using Formula:

Given, n = 12; n₁ = 6; n₂ = 4; n₃ = 2

Multinomial Coefficient = 12!/ (6! x 4! x 2!)

Multinomial Coefficient = (12 x 11 x 10 x 9 x 8 x 7)/(4! x 2!)

Multinomial Coefficient = (12 x 11 x 10 x 9 x 8 x 7)/(24 x 2)

Now, 12 x 8 = 96 and, 24 x 2 = 48

Since, 96/48 = 2 we get that,

Multinomial Coefficient = 11 x 10 x 9 x 7 x 2 = 13860