This is not HW just a practice question from the text.
Q.. (NOTE: I find that both part a and b say the same thing but the answers are different) Ten women attend a business luncheon. Each women checks her coast and a attache case. Upon leaving, each women is given a coast and case at random.
a. In how many ways can the coats and cases be distributed so that no woman gets EITHER of her possessions.
ans.$(d_{10})^2$ Would like to know why is this squared
b In how many ways can they be distributed so that no woman gets back both of her possessions.
ans. $n! * S(m,n)$ where $m= 2, n=10$ this ends up being equal to $0$ as $m<n$ (where $S(m,n)$ is stirling number of the second kind)
why are these two questions different and why is part a $(d_{10})^2$