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.

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.

anonymous · Answer

a) 12 songs any order=12!=479,001,600 ways.
b) 7 options for the first song, and then 6 options for the last song (because you can't play the first song over). Then, 10! ways to play the other 10 songs, so we have 7*6*10!=152,409,600 ways.
c) 5 options for song one, 4 for song two, 10! ways to play the other 10 songs, so we have 5*4*10!=72,576,000 ways.

amistre64 · Answer

12 songs to play. 
     7 slow songs
     5 fast songs

Each song is to be played only once. 

In how many ways can the disc jockey play the 12 songs if:

1.The songs can be played in any order. 

       12.11.10.9.8.7.6.5.4.3.2.1 = 12! = 479,001,600 ways

2.The first song must be a slow song and the last song must be a slow song. 

       ??

3.The first two songs must be fast songs.

    5.4 * 10.8.7.6.5.4.3.2.1  yep; 72,576,000