SOLUTION: Your drawer contains 8 red socks and 9 blue socks. It’s too dark to see which are which, but you grab two anyway. What is the probability that you get one of each color?

There are C(8,2) ways to get two red socks and C(9,2) ways to get two
blue socks.

That C(8,2)+C(9,2) = 28+36 = 64 ways to succeed.

There are C(17,2) = 136 ways to get any two socks.

So the probability is 64 out of 136 or  which
reduces to 

Edwin

Another way:

P[(red 1st AND red 2nd)  OR  (blue 1st AND red 2nd)]

AND means multiply and OR means add:

P(red 1st)×P(red 2nd) +  P(blue 1st)×P(red 2nd)] =

× + × = 

× + × =

 +  =  = 

Edwin