1. The Asbury Fun & Games Club has 23 members; 12 men and 11 women. They want to form a social committee with five members: two men and three women. How many different committees are possible?
2. In how many different-looking ways can the letters in the word "CHRISTMAS" be arranged?
3. The prizes in a raffle are a color television (first prize) and three MP3 players. Assuming that 500 people each bought one ticket, how many significantly different winner's lists are possible (assuming that the first name in the list won the first prize)?
4. In how many different-looking ways can the letters in the word "Committee" be arranged?
5. In how many different ways can a committee of five be chosen if the first person is the chairperson and the second person is the secretary of the committee? Assume that the committee is chosen from a group of 25 people.
6. A charitable organization sponsors a fund-raising raffle with six prizes: a color television, two radios, and three baseball caps. One thousand people each bought one ticket. In how many significantly different ways can the six winners be selected?