SOLUTION: on your phone you have 23 rap songs and 14 country songs. How many 6 song playlists (order matters) can you make that have 4 rap and 2 country songs

Question 1120433: on your phone you have 23 rap songs and 14 country songs. How many 6 song playlists (order matters) can you make that have 4 rap and 2 country songs
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I will assume "order matters" means the 6 different songs, and not just 4 rap and 2 country songs. In that case, the 6 songs can be arranged in 6!=720 different orders.

Then the number of ways you can choose 4 of the 23 rap songs is 23C4 = 8855 and the number of ways you can choose 2 of the 14 country songs is 14C2 = 91.

The total number of ordered playlists is then

720*8855*91 = 580179600
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