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We want to divide 10 dogs (including Fluffy and Nipper) into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs.  How many ways can we form the groups such that Fluffy is in the 2-dog group and Nipper is in the 5-dog group?

 Jan 13, 2023
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There are \({8 \choose 4} = 70\) ways to choose dogs for the group of 5. 

 

There are \({4 \choose 3} = 4\) ways to choose the dogs for the group of 3. 

 

Then there is \({1 \choose 1} = 1\) ways to choose the dogs for the group of 1. 

 

So, there are \(70 \times 4 \times 1 = \color{brown}\boxed{280}\)

 Jan 13, 2023

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