Challenge you

Probability Level 2

What is the coefficient of x 7 y 3 z 2 x^{7}y^{3}z^{2} in the expansion of ( x + 2 y + 3 z ) 12 (x+2y+3z)^{12} .


The answer is 570240.

Abdelhamid Khalil by Abdelhamid Khalil , 22, Morocco

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1 solution

展豪 張
Apr 9, 2016

Relevant wiki: Multinomial Coefficients

The coefficient is 12 ! 7 ! 3 ! 2 ! × 2 3 × 3 2 = 570240 \dfrac{12!}{7!3!2!}\times 2^3 \times 3^2=570240

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