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?
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 $\frac{14!}{5!}=\boxed{20,\!446,\!796,\!800}$.
