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Combinatorics

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Moderate

Quadruple Sum of Multinomial Coefficients

COMBIN-J5E41L

What is the value of the sum:

$$\sum {9\choose k_1, k_2, k_3, k_4} 2^{k_1}(-3)^{k_2}(-4)^{k_3}5^{k_4}$$

...where the summation is over all quadruples of nonnegative integers $(k_1,k_2,k_3,k_4)$ with $k_1+k_2+k_3+k_4=9$?

A

$-14^9$

B

$0$

C

$1$

D

$14^9$

E

none of the above