For a segment of a radio show, a disc jockey can play 9 records. If there are 14 records to select from, in how many ways can the program for this segment be arranged?

Answer 1

There are 14 choices for the first record played, then 13 choices for the second record played, then 12 choices for the third record played, and so on, until 6 choices left for the ninth and final record played. Thus there are $14\times 13\times 12\times \cdots \times 6$ ways to arrange the program. This product is equivalent to $\frac{14!}{5!}=\boxed{20,\!446,\!796,\!800}$.