Question

DJ Jacqueline is making a playlist for work; she is trying to decide what 9 songs to play and in what order they should be played. If she has her choices narrowed down to 6 jazz, 19 reggae, and 7 blues songs, and she wants to play an equal number of jazz, reggae, and blues songs, how many different playlists are possible

Answer 1

So, you want 4 of each kind.

Pick any set of 4 from each kind, and then there will be 12! ways to play them.

21C4 * 13C4 * 25C4 * 12! = 2.593*10^19