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?
+179 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.
