Number of totally ordered subsets of a set. Suppose I have set with n elements. How many different totally ordered subsets (tosets) does this set have? I know that this is the same as the sum from $k=0$ to $n$ of the permutations on k elements. However I believe this can be closed to a product. Is this correct? Thank you very much.
Regards.

I assume you mean a set with $n$ elements.  It sounds like you are not given an order, but allowed to choose the order, from you use of permutations on $k$ elements.  If so, you first have to select the $k$ elements from $n$, then permute them to make the order.
