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IN a certain zoom meeting, there are 4 students. How many ways are there to split them into any numbre of distinguishable breakout r ooms, each with at least 1 student?

 Jul 30, 2021
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In the diagram below, circles represent students and bars represent the "walls" of different rooms. 

 

We can see that there are 4 configurations of "bars". Zero bars, one bar, two bars, and three bars, which represent different ways to separate the students respectively. 

 

There are 3 slots that the bars can be in, so counting the different numbers of combinations for each of the scenarios gives $1 + 3 + 3 + 1 = \boxed{8}$

 

Alternativly, 1 + 3 choose 1 + 3 choose 2 + 3 choose 3 = 8 also works (if anyone knows how to type Combination in LaTeX, please tell me. 

 Jul 30, 2021

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