smc

Let the spider try to put on all $16$ things in a random order. Each of the $16!$ permutations is equally probable. For any fixed leg, the probability that he will first put on the sock and only then the shoe is clearly $\frac{1}{2}$. Then the probability that he will correctly put things on all legs is $\frac{1}{2^8}$. Therefore the number of correct permutations must be $\boxed{\frac{16!}{2^8}}$.