### Instruction: 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?### Response: To choose a pair of socks of different colors, I need to pick one sock from each of two different color groups.
I can do this in three ways: white and brown, white and blue, or brown and blue.
For each of these ways, I need to multiply the number of choices for each color.
For white and brown, I have 4 choices for white and 4 choices for brown, so 4 times 4 is 16.
For white and blue, I have 4 choices for white and 2 choices for blue, so 4 times 2 is 8.
For brown and blue, I have 4 choices for brown and 2 choices for blue, so 4 times 2 is 8.
To get the total number of ways, I need to add these three cases: 16 plus 8 plus 8 is 32.