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Miyu is giving out 9 identical chocolates to her 7 friends, including Dhruv.  All possible distributions are equally likely.  What is the probability that Dhruv gets exactly 2 chocolates?

 Feb 17, 2023
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Miyu is giving out 9 identical chocolates to her 7 friends, including Dhruv.  

 

Put the friends in order Dhruv can go first but it really doesnet matter

 

There will be  (9+7-1) C8 = 15C8  ways to distribute the chocolates

 

Now let Dvruv have her 2 chocs.

There are 6 friends left and 7 choc let so that makes     12C6 ways

 

So the likelyhood that Dvruv gets exactly 2 chocs is   

 

12C6  divided by  15C8  = 924/6435 = 28/195  which is approx   14.35% chance

 Feb 18, 2023

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