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?

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