Sum of the coefficients of the terms of degree m in the expansion of (1+x)n(1+y)n(1+z)n is

# Sum of the coefficients of the terms of degree m in the expansion of $\left(1+x{\right)}^{n}\left(1+y{\right)}^{n}\left(1+z{\right)}^{n}$ is

1. A

2. B

3. C

4. D

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### Solution:

We have

For sum of the coefficients of degree $m$, we must have
$r+s+t=m$ where $r,s,t$ are integers with $r,s,t\ge 0.$
Sum of such coefficients

$=$the number of ways of choosing a total number of m balls out of $n$ distinct black, n distinct white and $n$ distinct green balls
${=}^{3n}{C}_{m}$

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