Let
$x = \frac{n!}{(n-r)!}$
If the value of x and r is known to me how do I find the minimum value of n that will satisfy the equation? I tried simplifying the equation by plugging in
$\frac{n!}{(n-r)!}\ =\ (n-r+1)\ *\ (n-r+2)\ ....\ *\ n$
This will result in a polynomial equation but since the value of r can be quite large the degree of this polynomial equation can be very high, how am I supposed to proceed from here?