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Mr. Smith brings home 7 animals for his 7 children. Each child will adopt a pet to be her or his own. There are 4 different cats (a Siamese, a Persian, a Calico, and a Minx), 2 different dogs (a Poodle and a Golden Retriever), and a goldfish. Anna and Betty refuse to take care of the goldfish, and Charlie and Danny insist on having cats. The other 3 kids are easier to please -- they'll take anything. In how many ways can Mr. Smith give the children pets they'll want?

tertre  Feb 13, 2018
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Mr. Smith brings home 7 animals for his 7 children. Each child will adopt a pet to be her or his own. There are 4 different cats (a Siamese, a Persian, a Calico, and a Minx), 2 different dogs (a Poodle and a Golden Retriever), and a goldfish. Anna and Betty refuse to take care of the goldfish, and Charlie and Danny insist on having cats. The other 3 kids are easier to please -- they'll take anything. In how many ways can Mr. Smith give the children pets they'll want?

 

First we must make sense of this:

 

cat1, cat2, cat3, cat4,      Charlie and Danny and 2 others

Dog1, dog2,   

GoldFish                          NOT  Anna or Betty

 

I am going to attmept to allocat the pets in this order.

Charlie (4 cats), Danny (3 cat possibliities), Anna (4 non-fish pets left), Betty (3 non-fish left) , C5 (3 pets left), C6(2 pets left), C7 (this child gets what is left)

 

4*3*4*3*3*2*1 = 864 ways to allocate the pets.

Melody  Feb 13, 2018

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