If n is a positive integer such that
n!/(n-2)! = 342, find n.	Choose one:
A) 17  B) 18  C) 19  D) 20  E) 21
We write n! = n*(n-1)(n-2!)   Therefore   n!/(n-2)! = n(n-1)*(n-2)!/(n-2)! = n(n-1).   --&gt; n(n-1) = 342   --&gt; n^2 -n - 342 = 0   --&gt; n^2- 19n +18n -342 = 0   --&gt; n(n-19) +18(n -19) = 0   --&gt; (n-19)(n+18) = 0   Therefore n -19 = 0; n +18 = 0;   (i.e) n =19 ; n = -18   We want positive integer. So, n=19.   ANSWER:19
<result>C</result>
If n is a positive integer such that
n!/(n-2)! = 342, find n.