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

Question

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

a) -- 10 songs played in any order = 10!
b) -- first song is slow, and last song is slow
no. of ways = 7x8x7x6x5x4x3x2x1x6 = 42(8!)

c) frist 2 must be fast:
no. of ways = 3x2x8! = 6(8!)