Question

DJ Raven is making a playlist for an mp3 player; she is trying to decide what 11 songs to play and in what order they should be played. Step 2 of 2 : If she has her choices narrowed down to 7 reggae, 4 country, 6 blues, and 6 hip-hop songs, and she wants to play all 6 hip-hop songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answer 1

Total number of songs 7+4+6+6 = 23

Excluding hip hop songs number of songs remaining is 23 -6 =17

Since 6 hip hop songs are decided so we need to select 11 - 6 =5 songs out of 17 songs. Number of ways of selecting 5 songs out of 17 is

Now after 11 selecting 11 songs we need to decide order of selected songs in the playlist. Here we need to find possible permutation of 11 songs. The number of possible permutations is 11!.

So possible number of playlists are