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27 August, 21:19

DJ Ella is making a playlist for an internet radio show; she is trying to decide what 10 songs to play and in what order they should be played. Step 1 of 2 : If she has her choices narrowed down to 7 blues, 6 disco, 8 pop, and 4 hip-hop songs, and she wants to play no more than 4 disco songs, how many different playlists are possible

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  1. 27 August, 21:25
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    She can make up her 10 song playlist in 3195116 ways

    Step-by-step explanation:

    7 blues, 6 disco, 8 pop, 4 hip hops

    Total songs = 25

    She wants to play no more than 4 disco songs in a playlist of 10 songs

    Meaning the music can be grouped as disco and other music genres.

    Disco songs = 6

    Other genres = 19

    She can make up her 10 song playlist in any of the following ways.

    - 10 other genres, 0 disco song

    This playlist can be made in

    ¹⁹C₁₀ ways = 92378 ways

    - 9 other genres, 1 disco song

    This playlist can be made in

    ¹⁹C₉ * ⁶C₁ = 92378 * 6 = 554268 ways

    - 8 other genres, 2 disco song

    This playlist can be made in

    ¹⁹C₈ * ⁶C₂ = 75582 * 15 = 1133730 ways

    - 7 other genres, 3 disco song

    This playlist can be made in

    ¹⁹C₇ * ⁶C₃ = 50388 * 20 = 1007760

    - 6 other genres, 4 disco song

    This playlist can be made in

    ¹⁹C₆ * ⁶C₄ = 27132 * 15 = 406980

    Total number of ways = 92378 + 554268 + 1133730 + 1007760 + 406980 = 3195116 ways
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