How many combinations of puppies can he choose?

chanceandcade

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A potential breeder is buying puppies to begin his own business. Out of one litter of eight puppies he can choose any three puppies and out of a second litter of five puppies he may choose any two puppies. How many different combinations of puppies can he choose?

I get 560
 
Re: How many options?

Hello, chanceandcade!

A potential breeder is buying puppies to begin his own business.
Out of one litter of eight puppies he can choose any three puppies
and out of a second litter of five puppies he may choose any two puppies.
How many different combinations of puppies can he choose?
I get 560 . . . Right!

There are: (83)=56\displaystyle {8\choose3} \,=\,56 ways to choose 3 puppies from 8 puppies.
There are: (52)=10\displaystyle {5\choose2} \,=\,10 ways to choose 2 puppies from 5 puppies.

Therefore, three are: 56×10=560\displaystyle \,56\,\times\,10\:=\:560 ways to choose.

 
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