How many combinations of puppies can he choose?

[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

 

[soroban]

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

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

 

[tkhunny]

How did you get that? Show your work.

 

[chanceandcade]

how many options

8.7.6/3.2.1=56.6/6=56 etc?