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## Tunes for Cruising

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #14898 Fun: (2.5) Difficulty: (2.67) Category: Probability Submitted By: snaps

I recently burnt a CD with a selection of songs from my favourite rock bands to listen to in my car. The order of tracks, along with the bands that sing them, as burnt onto the CD are listed below (note: these songs and bands may sound similar to some more well-known songs and bands but that's purely coincidental).

1. Sourest Thing - V3
2. I Still Haven't Heard What I'm Listening For - V3
3. Without and With Me - V3
4. Son - Pearl Honey
5. Spin the White Square - Pearl Honey
6. Better Woman - Pearl Honey
7. Last Hug - Pearl Honey
9. Off He Comes - Pearl Honey
10. Finding Your Religion - M.E.R.
11. Nobody Hurts - M.E.R.

When driving along listening to this fine collection of tunes, I usually put my CD player on random (ie. the order that the tracks are played does not follow any set pattern). If my CD player plays through all 11 tracks before repeating any of them, what is the probability that no two songs from the same band will be played one after the other?

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 jimbo Sep 29, 2003 Excellent puzzle. I'm glad your tastes didn't run to one less V3 track and one more Pearl Honey track. That would have made it even more interesting! Hmmm. jacintan Oct 10, 2003 This is really good, but i think it should be put in the mathematical catogary. snaps Oct 10, 2003 The question asks for a probability. That's why it's in the probability category and not math. einat16 Oct 30, 2003 "purely coincidental" - LOL! good one (user deleted) Jan 05, 2004 Snaps, and any other people that love to made probability riddles I want to give you guys props, because it really takes thinking to come up with them, and that's probably why I haven't written one yet fg_4ever Jan 31, 2004 That was really HARD. But it was very interesting to see how the answer worked out. Probability was never one of my strong subjects. ghost09 Apr 11, 2004 I LOVE IT! CGauss6180 Oct 24, 2004 To be honest i found this the easiest question by far the other more wordy ones r harder so i agree this really is a math permutations question. snaps Oct 24, 2004 Let me state again that the question asks for the probability of something, hence the reason why it is in the probability category. tsimkin Nov 26, 2004 I agree that it belongs in the probability section. Combinatorics is frequently a part of probability. Good question, snaps! bbbz Aug 10, 2008 i had fun just figuring out the songs. "off he goes" came out when I was getting into blues, so that one stumped me at first. opqpop Sep 27, 2010 This is an easier question than it may seem. The key is to note a non-Pearl Honey songs must go in between each of the six Pearl Honey songs. Otherwise, it will be impossible to construct an order with no two consecutive songs being the same artist. The 5 non-Pearl Honey songs can be inserted in 5! ways. The 6 Pearl Honey songs can be rearranged in 6! ways. Hence there are 5! * 6! valid configurations. The total number of configurations is 11!. 5! 6! / 11! = 1/462