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Help I'm dying

 

Find the number of ways of placing 4 balls in 5 boxes if the balls are indistinguishable and the boxes are distinguishable.

 Jan 27, 2023
 #1
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First lay out the number of ways to distribute the 4 balls: 

 

4 - 0 - 0 - 0 - 0

3 - 1 - 0 - 0 - 0

2 - 1 - 1 - 0 - 0

2 - 2 - 0 - 0 - 0

1 - 1 - 1 - 1 - 0

 

For the first case, there are \({5 \choose 1} = 5\) ways to choose the box for the 4, and the rest must be 0

 

For the second case, there are \({5 \choose 3} \times {2 \choose 1} = 20\) ways.

 

For the third case, there are \({5 \choose 1} \times {4 \choose 2} = 30\) cases

 

For the fourth case, there are \({5 \choose 2} = 10\) cases. 

 

For, the final one, there are \({5 \choose 1} = 5\) ways. 

 

So, in total there are \(5 + 5 + 10 + 20 + 30 = \color{brown}\boxed{70}\) ways.

 Jan 27, 2023
 #2
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Incorrect answer.

Guest Jan 31, 2023

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