Question

A disc jockey has 10 songs to play. Four are slow songs, and six are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 10 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

if there are no restrictions, ten choices for first song, nine for second, 8 for third ...
counting principle tells you that there are
\[10!=10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\] ways do do this

Answer 2

first and last are slow is no different than first and second are slow
that would be \(4\times 3\times 8\times 7\times 6\times 5\times 4\times 3\times 2\)

Answer 3

OK GOT IT THANKS YOU'VE BEEN VERY HELPFUL

Answer 4

THE FIRST TWO SONGS MUST BE FAST SONGS DO I MULTIPLY6*5*4*3*2