help me to solve this ps problem

Solution:
nPr is n!/(n-r)! and nCr is n!/{r!*(n-r)!}.
So nPr/nCr is r! which is 30240/252 = 120 = 5!
So r is 5.
We need not look for n because in all options there is only one choice where r is 5.

Correct answer is (10,5).

this problem is not remotely similar to anything that you will ever see on the gmat.
not even close. like, not even within shouting distance.

if this problem was actually taken from a set that was designed for the gmat, then i would bet good money that the entire set is a waste of your time. stay away!
if the author is actually pushing this as a gmat preparation problem, then it's clear that he/she has never actually laid eyes on the gmat.

if you are taking problems from sets that were not designed for the gmat -- which i certainly hope is the case here -- then you might want to think twice about whether you have already reviewed the official materials carefully and thoroughly enough to justify branching out to such tangentially relevant materials.