ILL 1986 Problem 10

A set of $n$ standard dice are shaken and randomly placed in a straight line. If $n < 2r$ and $r < s$ , then the probability that there will be a string of at least $r$ , but not more than $s$ , consecutive $1$ 's can be written as $\frac{P}{6^{s+2}}$ . Find an explicit expression for $P$ .