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.