Question

If $n$ is a factor of $72,$ such that $xy=n$ then number of ordered pairs $\left(x , y\right)$ are :- (where $x,y\in N$ )

Answer 1

Let $xyz=72=2^{3}\times 3^{2}$
then number of solutions are ${}^{3 + 3 - 1}C_{3 - 1}^{}\times {}^{2 + 3 - 1}C_{3 - 1}^{}$
$={}^{5}C_{2}^{}\times {}^{4}C_{2}^{}=10\times 6=60$