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math challenge I-C hw

 
 
Picture of Yizhou Zhang
math challenge I-C hw
by Yizhou Zhang - Wednesday, 22 April 2020, 7:56 PM
 

for chapter stars and bars number 14, I am confused about which one to choose, none of them look right to me.

 
Picture of Areteem Professor
Re: math challenge I-C hw
by Areteem Professor - Thursday, 23 April 2020, 10:44 AM
 

Think of this equivalent version of the problem: You have 6 boxes numbered $1$ through $6$, you have $2$ balls inside of the box numbered 1, $3$ balls inside of the box numbered $4$, and $1$ ball inside the box numbered $5$.

If you have the boxes lined up next to each other (in order), you can think of the bars as the sides of the boxes that touch, for example, if you wanted $3$ balls inside box $2$, $4$ balls inside box $5$ and $1$ ball inside box $6$, the arrangement of stars and  bars would look like: $$| ***|||****|*$$