a lawyer has five clients--a, b, c, d, and e--that she must meet on wednesday, thursday, and friday. she must meet at least one client each day. she cannot meet b and e on the same day. she meets d on wednesday. she meets exactly two clients on friday.
if the lawyer meets c on thursday, how many different arrangements of clients to days are possible for the week?
4
the lawyer must meet d on wednesday and c on thursday. furthermore, she must meet a on friday because two clients must be scheduled for friday, and they can't be b and e. so, we have to figure out where b and e can go. they can be scheduled for wednesday and friday or for thursday and friday, and they can go in either order (b-e or e-b) on those two days. that's a total of four different possibilities for the week.