Dan Jones, was a classmate of Shawn Fanning, at Northeastern, and made early use of Fanning's Napster to download 300 MP3s.
The collection he dowloaded contained:
Hip-hop 47
Heavy Metal 59
Rock 80
Punk 54
Reggae 46
Celtic Folk 14
Now known as "DJ Dan", he hosts a radio show on WPRS, a pirate radio station that broadcasts from a dinghy off the coast of Nantucket. Six songs with a lot of chat fills his half hour of daily air time. If two programs are considered the same only if he plays the same songs in the same order, how many different programs can DJ Dan offer if
he plays 1 Hip-hop and 5 Celtic Folk MP3s, with no repetition?
+128578 We can first count sets and then arrangements of those sets
We want to choose 1 of the 47 hip-hop MP3s and any 5 of the 14 Celtic Folk MP3s
The total number of sets of songs is given by C(47,1)* C(14,5) = 94094
But......each set of songs can be arranged in 6! = 720 ways
So 94094 x 720 = 67,747,680 different programs
+128578 We can first count sets and then arrangements of those sets
We want to choose 1 of the 47 hip-hop MP3s and any 5 of the 14 Celtic Folk MP3s
The total number of sets of songs is given by C(47,1)* C(14,5) = 94094
But......each set of songs can be arranged in 6! = 720 ways
So 94094 x 720 = 67,747,680 different programs
