Question

Show all work. A disc jockey has 12 songs to play. Seven are slow songs, and five are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 12 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

the songs can be played in any order is simply 12!

Answer 2

what bout the rest

Answer 3

for "The first song must be a slow song and the last song must be a slow song" it is just
7 x 10! x 6 because the first slow song has 7 options and so the last one has 6 slow options left and the rest of the other total songs is 10!

Answer 4

The first 2 mast be fast:
5C2 * 10!