+0  
 
0
69
3
avatar+278 

How many ways are there to put 2 white balls and 2 black balls into 3 boxes, given that balls of the same color are indistinguishable, but the boxes are disti nguishable?

 

Work: 
Put first the P white balls into the N different boxes which can be done in (P+N−1,P)
,then for each of these you do the same with the black balls so overall the answer is (P+N−1,P)(Q+N−1,Q) so the answer should be (5,2)*(5,2)

(5, 2) = 5!/(3!*2!) = 10

10*10 = 100

 

Please help check. Thank you

 Mar 24, 2020
edited by Guest  Mar 24, 2020
 #1
avatar+111330 
+1

Let  k  be  the  number of  balls  and  the number of  boxes =  n

 

The "formula"  for this  is  :

 

C ( n + k - 1, n - 1)   

 

I agree with your methodolody

 

I believe that the  answer  should be

 

[C ( 3 + 2 - 1, 3 - 1 )]^2 =  [ C(4,2)]^2  = 6^2   =  36  

 

 

cool cool cool

 Mar 24, 2020
 #2
avatar+1970 
+2

Nice, Chris!

CalTheGreat  Mar 24, 2020
 #3
avatar+278 
0

Great work! Well done!

 Apr 2, 2020

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