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10-5 - DJ Ali is making a playlist for a website she is...

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Unformatted text preview: DJ Ali is making a playlist for a website; she is trying to decide what 13 songs to play and in what order they should be played. If she has her choices narrowed down to 8 reggae, 6 blues, 6 hip-hop, and 7 rock songs, and she wants to play all 7 rock songs, how many different playlists are possible? Write your answer in scientific notation. Begin by thinking of this problem as a Fundamental Counting Principle problem. Overall, there are two slots to fill—a slot for choosing the 13 songs for the playlist and a slot for determining the order in which the selected songs will be played. We will focus on calculating the number of ways to choose the songs for the playlist first. Determining the number of different ways to choose the songs for the playlist is also a Fundamental Counting Principle problem. There are two slots to fill—a slot for choosing the rock songs and a slot for choosing the rest of the songs needed for the playlist. We will use the combination formula to calculate the number of ways to choose the 7 rock songs and the other 13 — 7 = 6 songs since the order in which the individual songs are chosen does not matter. ...
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