Question

Lucy is planning to run for an hour, and she's using her iPod for the countdown, so she has to create a 60-minute playlist.

Her iPod contains:

six 5-min songs;
five 6-min songs;
four 8-min songs.
Count the number of possibles playlists where the order doesn't matter.

Answer 1

\[60 \div 8 = 7.5\text{ 8 minute songs}\]

Answer 2

\[\text{This is only one possible playlist, btw}\]
We only have four 8 minute songs, so now we need a value that makes up the rest (3.5 eight-minute songs)

Answer 3

I guess that's not kind of right

Answer 4

I'm working on actually getting all the results.
\[\text{A mafia boss must be patient. ;) }\]

Answer 5

Okayyy :)

Answer 6

(I forgot how to do this so I asked someone else I'm sorry ; o; )

Answer 7

Seems like a combination/permutation like problem.

Answer 8

I was thinking that too, but I suck at those. ; o;
@Jhannybean

Answer 9

Say she puts \(a\) number of 5-min songs,
\(b\) number of 6-min songs and
\(c\) number of 8-min songs in her playlist.

then we need to solve below equaiton in integers :
\[5a+6b+8c = 60\]
\(0\le a\le 6\)
\(0\le b\le 5\)
\(0\le c\le 4\)

Answer 10

Notice \(a\) cannot be an odd number because that evaluates the left hand side to an odd number. so \(a\) can only take values : \(\{0,2,4,6\}\)

Answer 11

Thank you for saving the day @ganeshie8 ! T ^T

Answer 12

Wow never thought of that. Then what could have been the next? Sorry late reply