Question

If the papers of $4$ students randomly distributed for checking among $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is $\frac{n}{m}$ where $n,m$ are natural numbers and $HCF(n,m)=1$. Then the number of positive divisors of $(n+m)$ is

Answer 1

$P\left(E\right)=\frac{{}^7{C}_2\times (2^4-2)}{7^4}=\frac{21\times 14}{7\times 7\times 7\times 7}=\frac{3\times 2}{49}=\frac{6}{49}$
$\Rightarrow n+m=55$ \
Positive Divisors of $55$ are $\to 1,11,5,55$