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8 November, 22:21

Twenty rock songs and 18 rap songs are in a disc jockey's library. During a radio show how many

different orders can the songs be played if the playlist consists of 8 rock songs and 6 rap songs?

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  1. 9 November, 00:51
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    Answe4.516439288 x 10²² ways

    Step-by-step explanation:

    The number of ways the songs in the playlist can be played involves a permutation, since order is involved.

    8 rock songs can be played out of 20 in:

    20P8 ways = 20! / (20-8) !

    = 20!/12! = 6.033983155 x 10^13 ways

    Similarly, 6 rap songs can be played from 18 in:

    18P6 ways = 18! / (18-6) !

    = 18!/12! = 8.892185702 x 10^12 ways

    Hence, the number of ways 8 rock and 6 rap songs can be played from the disc's library is a multiplication of both permutations, which yields:

    4.516439288 x 10²² ways
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