+0  
 
0
11
1
avatar+1351 

In how many ways can you distribute $8$ indistinguishable balls among $5$ distinguishable boxes, if at least three of the boxes must be empty?

 Mar 23, 2024
 #1
avatar+128794 
+1

2 boxes  with balls in them

 

Choose  2 boxes of the 5 =  C(5,2)  = 10 ways of  selecting the boxes

Ball splits             Ways to distribute the balls

7  1                                  2

6  2                                  2

5  3                                  2

4  4                                  1

2 * 2 * 2 * 1  =  8 ways

So   10 * 8  = 80 ways

 

1 box with all 8 balls  =  5 ways to  do  this

 

Total ways

 

80  +  5  =   85

 

cool cool cool

 Mar 24, 2024

5 Online Users

avatar
avatar
avatar
avatar