jmc

Question

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?

Accepted Answer

Charlie can take one of the 4 cats, and Danny can take one of the 3 remaining cats, so there are 4 3=12 ways to give cats to these two kids. Since Anna and Betty can't take a goldfish, they select from the 4 remaining animals so there are 4 3=12 ways to give pets to these two kids. For the other three kids, there are 3 2 1=6 ways to give out the remaining 3 pets. The answer is 12 12 6=864.