The question: Sally has $N$ friends and likes to invite them over in small groups for dinner. She calculated that she can invite a different group of $3$ friends to dinner at her house every night for a year. What is the minimum number of friends Sally can have?
Use $365$ for days in a year; leap-year does not have to be considered.
We know $k=3$, so $\binom{n}{3}=\frac{n!}{3!(n-3)!}=\frac{n!}{6(n-3)!}=365$
$\frac{n!}{(n-3)!}=2190$
I get stuck at $n!=2190(n-3)!$
I assume that this is the next step in the process. What do I do from here?