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December 10th, 2008, 01:20 PM  #1 
Newbie Joined: Dec 2008 Posts: 8 Thanks: 0  interesting probability question
I was wondering what the formula would be to figure out this problem i thought of. If you have a CD with 19 songs on it and you play it on shuffle what would the probability be of it playing the CD in the correct order. Ignore the fact that the shuffle feature is faulty on MP3 players. It is just an example. 
December 10th, 2008, 01:29 PM  #2 
Newbie Joined: Dec 2008 Posts: 8 Thanks: 0  Re: interesting probability question
Would it be a permutation? 19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1= 121645100408832000 
December 10th, 2008, 02:13 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: interesting probability question
1/19! ??

December 10th, 2008, 02:54 PM  #4  
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: interesting probability question Quote:
 
December 10th, 2008, 03:12 PM  #5  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: interesting probability question Quote:
In regards to the question: My reasoning is as follows. At the start of playback there are 19 possibilities and only one is the first track, so the probability of it being played is 1/19. For the next song there are 18 possibilities and only one is the second track so the probability of it being played is 1/18. From my rather limited understanding of probability, this means that the odds of the first track being played first followed by the second track are 1/(18 * 19) or 1/342. Extending this pattern gives (I think) 1/19! or 8.22063525 X 10^18. It is rather a slim chance, according to these numbers, but then, I could be wrong, of course.  
December 10th, 2008, 03:14 PM  #6 
Newbie Joined: Dec 2008 Posts: 8 Thanks: 0  Re: interesting probability question
for the sake of the question lets assume that there are no repeats.

December 10th, 2008, 03:33 PM  #7 
Newbie Joined: Dec 2008 Posts: 8 Thanks: 0  Re: interesting probability question
would that be for the whole cd of 19 songs? The 1/19 would only apply for the 1st song being played in the correct order. for all 19 songs it would be: 1/(19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)= 1.21645100408832e+17 (I think) 
December 10th, 2008, 03:46 PM  #8  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: interesting probability question Quote:
 
December 10th, 2008, 03:58 PM  #9 
Newbie Joined: Dec 2008 Posts: 8 Thanks: 0  Re: interesting probability question
I did not know that the !=factorial you learn something new every day 
December 10th, 2008, 04:10 PM  #10 
Newbie Joined: Dec 2008 Posts: 8 Thanks: 0  Re: interesting probability question
1/(19!)=8.22063524662433e18 thank you 

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