Combinatorics: Restricted Permutations This is the problem I am trying to solve: `You are rearranging your bookshelf to make it more interesting and harder to find anything on it. On one of the shelves you plan to put 11 biographies and 6 mysteries. How many ways can you arrange them on the shelf if you don't want any two mystery books next to each other (i.e. they need to be separated by at least one biography, maybe more...).` The solution is $P(11,11) * P(11+1, 6)$ $P(11,11)$ represents the number of arrangement possible of the biography books on the shelf but what does $P(11+1, 6)$ represent? And how do I count the arrangements possible by the restriction of having at least 1 biography book in between every mystery book?

$P(11+1,6)$ represents the 12 spots to place the 6 mystery books as there is before the first biography and after each one that represents the 12 slots for the mystery books to go.

If necessary, consider this picture:

_ A _ B _ C _ D _E _ F_ G _ H _ I _ J _ K _

Where the dashes are places for a mystery book and A-K represent the 11 biography books.