1. A designer of a window display wants to form a pyramid with 15 hats. She wants to place the five men's hats in the bottom row, the four women's hats in the next row, next the three baseball caps, then the two berets, and a clown's hat at the top. All of the hats are different. How many displays are possible?
2. In how many ways can five people be assigned to seats in a 12-seat room?
3. A poker hand consists of five cards. How many different poker hands contain all cards of the same suit? (Such a hand is called a "flush.")