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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?

 Dec 1, 2022
 #1
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We have  10 dogs in the following groups

 

fluffy plus 1 more

Nipper plus 4 more

A group of three.

 

8C3 ways to choose the 3  then 5 ways to get the one  the rest go in with nipper

 

8C3 *5 =  56*5 = 280 ways

 Dec 1, 2022

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