# 10-4 - 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 no more than 3 blues songs, how many different playlists are possible? Write your answer in scientiﬁc notation. Now we need to determine the number of different ordered arrangements for all of the songs chosen. For this second slot in our counting problem, order is important, so we will be using the permutation formula. The number of permutations of all 13 songs chosen for the playlist is 13! 13! 13! P — — — 6227020800. 1313—03—13)! 0! 1 Finally, according to the Fundamental Counting Principle, we multiply the number of possibilities for each slot to get the answer. Therefore, the number of different possible playlists is (6C0 - 21C13 + 6C1 - 21C12 + 6C2 - 21C11+ 6C3 - 21C10)- l3Pl3 = 14312130 - 6227020800 22 8.91 >< 1016 Answer: 8.91 X 1016 ...
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