Question

If number of terms in the expansion of $(x+2y+3z{)}^n$ are $45$, then $n$ is equal to -

• A. $7$
• B. $8$
• C. $9$
• D. None of these

Answer 1

The correct option is B $8$

$(x+2y+3z{)}^n$

No of terms in ${(x_1+x_2+\dots +x_r)}^n$

are ${}^{n+r-1}{C}_{r-1}$

So mo of ternss in $(x+2y+3z{)}^n={}^{n+2}{C}_2$

So ${}^{n+2}{C}_2=45$

$\frac{\mid n+2}{\mid n\left(2\right)}=45$

So $(n+2)(n+1)=90$

$\therefore n=8$