Question

If the number of terms in the expansion of $(x+y+z{)}^n$ is $36$, then the value of $n$ is

Answer 1

Given expansion $(x+y+z{)}^n$

The number of terms is
${}^{n+3-1}{C}_{3-1}=36\Rightarrow {}^{n+2}{C}_2=36\Rightarrow \frac{(n+2)(n+1)}{2}=36\Rightarrow n^2+3n+2=72\Rightarrow n^2+3n-70=0\Rightarrow (n+10)(n-7)=0\Rightarrow n=7(\because n\in N)$