I have 10 distinguishable socks in my drawer: 4 white, 4 brown, and 2 blue. In how many ways can I choose a pair of socks, provided that I get two socks of different colors?
We have 3 different combinations we can make
1.) White and Brown: \(4\cdot4=16\) ways
2.) Brown and Blue:\(4\cdot2=8\) ways
3.) White and Blue: \(4\cdot2=8\) ways
So if we add all of the ways we get \(16+8+8=32\) different ways
Hope this helps!