# Factorials



## vavaving (Apr 20, 2009)

Interestingly enough, a meer 10 tracks sorted into every possible sequence would yield over 3 million playlists! 
What not to do in your spare time.


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## bassClef (Oct 29, 2006)

Here's another one for you : get 23 people in a room and there's a 50% chance two of them will share the same birthday.


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## Nicola (Nov 25, 2007)

vavaving said:


> Interestingly enough, a meer 10 tracks sorted into every possible sequence would yield over 3 million playlists!


If the number of tracks were extended to 13, that would be enough to provide 93% of the world's entire population with their own unique playlist. If it were extended to 14 tracks that would suffice to give each person in the world some 13 playlists.

The problem with this is that if the order in which tracks are played is ignored there is only one playlist per set of tracks if all tracks are played. In order to generate over 3 million playlists each of 10 items where the order does not matter, it would necessary to have 25 tracks to start with.



jezbo said:


> Here's another one for you : get 23 people in a room and there's a 50% chance two of them will share the same birthday.


I make it 20 people on the basis that there are 190 combinations of 2 people from 20, which generates a 52% probability that any two will share a birthday. With 23 people, the probability of a shared birthday increases to 70%.

In order to achieve a 50% chance that any three people will share the same birthday the minimum number of people in the room needs to be 75; for four people it needs to increase to 147 people; for five shared birthdays, 256 people; for six shared birthdays, 366 people, for 7 shared birthdays, 483 people (ignoring problems about leap year birthdays).


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## bassClef (Oct 29, 2006)

I didn't try to work it out - I read it somewhere 

EDIT: This backs me up, so you might have your sums a bit wrong:
http://en.wikipedia.org/wiki/Birthday_paradox


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