Ten women attend a business luncheon. Each woman checks her coat and attache case. Upon leaving, each

Question:

Ten women attend a business luncheon. Each woman checks her coat and attache case. Upon leaving, each woman is given a coat 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?
(b) In how many ways can they be distributed so that no woman gets back both of her possessions?