Permutations Involving 8 Elements

How many permutations $$\tau$$ on 8 elements are there such that $$\tau \circ \tau$$ is the identity permutation?

Details and assumptions

You may think of a permutation on 8 elements as a way to shuffle a deck of 8 cards. The identity permutation would correspond to the shuffle where we do nothing (hence it stays the same = identity). If $$\tau$$ corresponds to only exchanging the top 2 cards, then $$\tau \circ \tau$$ would return the deck to it's unchanged state.

×