Di is making a playlist for work, she is trying to decide what 10 songs to play

Question

Di is making a playlist for work, she is trying to decide what 10 songs to play and in what order they should be played. If she has a choices narrowed down to 6 hip hop, 5 pop, 6 blues and 5 reggae songs and she wants to play no more 3 hip hop songs. How many different playlists are possible? Di is making a playlist for work, she is trying to decide what 10 songs to play and in what order they should be played. If she has a choices narrowed down to 6 hip hop, 5 pop, 6 blues and 5 reggae songs and she wants to play no more 3 hip hop songs. How many different playlists are possible?

Explanation / Answer

Since order Matter, this is a question on Permutations: She has 6 Hip hop songs and 16 other types of songs(reggae, blues and pop)

No more than 3 means she can play 0 Hip Hop and 10 others or 1 Hip Hop and 9 others or 2 Hip hop and 8 others or 3 Hip hop and 7 others, i,e

(6P0 x 16P10) + (6P1 x 16P9) + (6P2 x 16P8) + (6P3 x 16P7) = 29059430400 + 24908083200 + 15567552000 + 691891200 = 70226956800

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