Question

A disc jockey has 9 songs to play. Five are slow songs, and 4 are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 9 songs if
The songs can be played in any order.
The first song must be a slow song and the last song must be a slow song.
The first two songs must be fast songs.

Answer 1

any order then there are 9 choices for first, 8 for second, 7 for third etc
counting principle says multiply all these together to get
\[9!=9\times 8\times 7\times 6\times5\times 4\times 3\times 2\]

Answer 2

if the first and last song must be slow, it is the same as saying first and second must be slow
number of ways is \(4\times 3\) for the first two, then \(7\times 6\times 5\times 4\times 3\times 2\) for the rest
multiply these together for your answer