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!

I struggled with the above explanations so came up with the following: 40 socks total, 8 socks per colour.


*

*2 draws


I draw one red: chances are 8 / 40
I draw a second red: 7 /39 => second draw is dependant from first so i need to multiply chances of the two draw: 8/40 * 7/39 = 56 / 1560.
Same reasoning applies for the other colours so I can multiply by 5 my previous result: 5 x 56 /1560 = 280 / 1560 


*

*3 draws


Using the red socks, i have the following combinations when drawinf three times:


*

*1 red then 1 red then 1 non-red

*1 red then 1 non-red then 1 red

*1 non-red then 1 red then 1 red

*1 red then 1 red then 1 red


probability will be respectively:


*

*(8/40 * 7/39 * 32/38) +

*(8/40 * 32/39 * 7/38 ) +

*(32/40 * 8/39 * 7/38 ) +

*(8/40 * 7/39 * 6/38 ) 

*= 1,792 / 59,280 * 3 + 336 / 59280 = 7,504 / 59280


All colours have the same numbers so we can multiply by 5 so: 5 * 7,504 / 59,280
Same work can be done for 4 and 5 draws although factoring it is tempting and quite easy.
