Probability of getting a pair of socks from a drawer if three are drawn I'm really struggling with this concept, hoping you guys could help me out.
Question: You have been provided with 20 pairs of socks within a box consisting of 4 red pairs, 4 yellow pairs, 4 green pairs, 4 blue pairs and 4 purple plairs.
The pairs have been separated out and you must take out a pair of socks.
Consider these problems and provide a calculation for each: 


*

*Probability of drawing a matching pair if you randomly draw 2 socks?

*Probability of drawing a matching pair if you randomly draw 3 socks?

*(Repeats up to randomly drawing 5 socks)


For 2 socks I got the following:
40 possible socks * 39 other possible socks = 1560 possible combinations of socks / 2 (to remove duplicate matches) = 780
For each set of socks, there are 8. 8 * 7 (7 other socks to each being matched) = 56 possible combinations in each set of socks / 2 to remove duplicates = 28 possible combinations of socks in each set.
28 / 780 = 0.036 probability of drawing a pair when drawing 2 socks from the drawer.
I'm completely lost when it comes to drawing three socks from the drawer, however - 
Cheers guys!

HINT: with 3 socks you must find the probability that all socks have different color, the probability that 2 socks have the same color, and the probability that all socks have the same color. Name these probabilities as P1, P2 and P3... with the number referencing the different amount of different colors.
For any number of socks there is the same strategy: probability for different amount of different colors, i.e. for 5 socks you want to know P1, P2,..., P5.
After you do that then you must multiply each probability for the probability of get at least one sock of one of the colors for this group. "At least one" is the opposite to "no one" but this last probability is easier to calculate, after you get the complementary that is the probability that you are searching.
After you did that you sum all these multiplications and voilá!, its done.
