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

Answer: 60

Let $xyz=72=2^3\times 3^2$
then number of solutions are ${}^{3+3-1}{C}_{3-1}^{}\times {}^{2+3-1}{C}_{3-1}^{}$
$={}^5{C}_2^{}\times {}^4{C}_2^{}=10\times 6=60$