Dj jill is making a playlist for work; she is trying to decide what 12 songs to play and in what order they should be played. step 2 of 2 : if she has her choices narrowed down to 3 jazz, 6 blues, 7 disco, and 5 country songs, and she wants to play all 6 blues songs, how many different playlists are possible?

Respuesta :

2.3974x[tex]10^{12}[/tex] are the number of ways that different playlists are possible

Number of ways in which 12 songs can be selected from 3 jazz, 6 blues, 7 disco and 5 country songs such that all 6 blues are selected

= 6C6 x Number of ways from 3 jazz, 7 disco, and 5 country tracks to choose the final 6 songs

= 6C6 x 15C6

= 1 x 5005

= 5005

Number of playlists possible = Number of song combinations x Number of orders in which they can be arranged

= 5005 x 12!

= 2.3974x[tex]10^{12}[/tex]

Consequently, there are 2.3974x[tex]10^{12}[/tex]  numerous methods in which different playlists can be created.

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