Suppose that I have 6 different books, 2 of which are math books. In how many ways can I stack my 6 books on a shelf if I do not want the math books to be at the ends?
For the first end, there are four choices; 6 books minus the 2 math books.
For the second end, there are three choices; 6 books minus the 2 math books and the first end.
For the middle four, there are 4! choices, which is just 24.
\(24 * 4 * 3 = 288\)
(My counting has always been bad and time has probably not helped it. There's a pretty good chance I did something wrong.)