Aspider has one shoe and one sock for each of its eight legs. in how many different orders can the spider put on its socks and shoes, assuming that on each leg the sock must be put on before the shoe? (for avoidance of doubt, a spider will not be putting its 5th leg sock on its 3rd leg.)

The probability to put sock and shoe on all legs is 1/2^8. Therefore the number of correct permutations must be 16!/2^8.

Explanation:

There are two actions for each leg - the sock and then the footwear. All we need to know is to determine a sequence when each leg has been worked on. That is 16/2 for the first section, 14/2 for the second, and so on...

Equivalently, the multinomial coefficient would be (16/2,2,…, 2) = 16!/2^8.

answer; automated fingerprint;