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How many ways are there to put 5 balls in 2 boxes if the balls are distinguishable and the boxes are distinguishable?

 Aug 3, 2022
 #1
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By stars-and-bars, there are 15 ways.

 Aug 3, 2022
 #2
avatar+113 
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Well, how many balls can be placed in each box?

 Aug 3, 2022
 #3
avatar+124596 
+2

Assuming  a box could be empty

 

Choose all 5 balls to go into  either box  - the other box is empty by default

C(5,5) * 2             =    2 ways

Choose  4 of the 5 balls to go into either box  -  the remaing ball goes into the other box by default

C(5,4)  *2            =    10   ways

Choose 3 of the 5 balls  to go into either box -  the remaining two balls go into  the other box by default

C(5,3) * 2             =   20 ways

 

32 ways 

 

 

cool cool cool

 Aug 3, 2022

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