kenzbenz01
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DJ Giovanni is making a playlist for a friend; he is trying to decide what 12 songs to play and in what order they should be played. If he has his choices narrowed down to 22 country, 11 reggae, and 5 pop songs, and he wants to play an equal number of country, reggae, and pop songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Respuesta :

MathPhys

Answer:

5.78Ɨ10Ā¹āµ

Step-by-step explanation:

The playlist has 12 songs, and he wants the same number of songs for each genre, so he must pick 4 songs per genre.

The number of ways he can choose 4 country songs (ignoring the order) is ā‚‚ā‚‚Cā‚„ = 7315.

The number of ways he can choose 4 reggae songs (ignoring the order) is ā‚ā‚Cā‚„ = 330.

The number of ways he can choose 4 pop songs (ignoring the order) is ā‚…Cā‚„ = 5.

The total number of combinations is 7315 Ɨ 330 Ɨ 5 = 1.21Ɨ10ā·.

Once he has his 12 songs selected, the number of ways he can arrange them is ā‚ā‚‚Pā‚ā‚‚ = 12! = 4.79Ɨ10āø.

So the total number of possible playlists is:

(1.21Ɨ10ā·) Ɨ (4.79Ɨ10āø) = 5.78Ɨ10Ā¹āµ

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