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!


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.

So $40$ socks in total.  $8$ of each among $5$ colours.


*

*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)


It is easier to evaluate the probability for the complement: that of drawing no matching colours.
So the probability for drawing a matching pair when drawing two socks is:
$$p_2= 1-\dfrac{\dbinom 52\dbinom 81^2}{\dbinom{40}2}$$
And likewise for the rest.
