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Marvin randomly places 7 Scuba Steve action figures and 6 Diving Dan action figures in 4 distinguishable boxes. If each box must have at least one of each type of action figure, how many ways can Marvin do this?

 Oct 1, 2022
 #1
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After we put 1 of each action figure in each box, there are 3 Scuba Steves and 2 Diving Dans left.

 

Using stars and bars for the number of Scuba Steves gives us 3 stars and 3 bars, for \({6 \choose 3} = 20\) combinations

 

Doing the same thing for the Diving Dans gives us 2 stars and 3 bars for \({5 \choose 3} = 10\) combinations.

 

So, there are \(20 \times 10 = \color{brown}\boxed{200}\) ways to do this.  

 Oct 1, 2022

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