Yvonne wants to invite seven of her twenty classmates to her birthday party. She and her classmates will all be seated at the above table. Which of the following expressions gives the number of ways she can select seven classmates and seat them, and herself, at the table?

Mr. and Mrs. Williams have invited three other married couples to a dinner party; the eight are to be seated at the table shown above. Since Mr. and Mrs. Williams need to be close to the kitchen so that they can serve the meal, it is desired that they sit at Seats 1 and 8, although it does not matter which one sits in which seat. There are no other restrictions.

How many ways can the eight persons be seated to fit this specification?

If a team of 7 basketball players win a game and each high-five each other once after a game, how many high-fives take place?

Mr. and Mrs. Jones have invited three other married couples to a dinner party; the eight are to be seated at the table shown above. It is desired that each husband sit directly across from his wife -for example, a husband at Seat 1, his wife at Seat 6.

How many ways can the eight persons be seated to fit this specification?