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Cheap 'n' Nasty MP3 Player

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

 

Puzzle ID:#20784
Fun:*** (2.62)
Difficulty:*** (2.2)
Category:Probability
Submitted By:pi202****
Corrected By:Winner4600

 

 

 



My MP3 player is cheap 'n' nasty and has now broken: it is stuck on 'Shuffle'. In this mode it starts with whatever track you put it on, but then plays tracks in a random order. The only restriction is it never plays a song that's already been played that day.

I purchased my favourite murder mystery book in audio format, and put the first 6 chapters on my MP3 player. (Each chapter is exactly 1 track.) There's nothing else on my player at the moment. What is the probability that I will hear the 6 chapters in order as I listen today, without having to change tracks at all? (Obviously, I will ensure it plays chapter 1 first.)

The next day I empty the player before putting on the next 6 chapters. This time I also transfer a CD of mine with 11 songs on. I don't mind songs coming in between the chapters of my book, as long as the chapters are in order. What's the probability of that happening now?


Answer

With only 6 tracks on the player:
The first chapter has been set to play first. The probability of the next 5 chapters playing in order is 1/5! = 1/120.

With the music on the player as well:
Seeing as I don't care about when the music plays, it doesn't change anything. The answer is still 1/120.

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