The numbers don't add up in this Venn diagram? 
I'm trying to draw a Venn diagram to make sense of the overlapping 3 pairs of brightly colored and stripped socks but the numbers don't add up to the 10 pairs given in the question? How can there be 10 pairs of socks?

 A: There can also be socks that are neither brightly colored nor striped. 
A: You are correct - the numbers do not add up.  If we have 10 pairs and 6 brightly coloured and 4 striped - this immediately implies that there can be none with both characteristics.
A: (https://imgur.com/a/nYVpRPm)
I copied your diagram and added. The universe U for the Venn diagram is the total socks (which is 10).  There is part in the venn diagram which is neither brightly colored or striped (denoted by A in the venn diagram). In this case, to calculate A, the total socks is 10 so

$$A + 1 + 3 + 3 = 10$$
$$A = 3$$
So, the probability to wear colored or striped socks in first day is
$$\frac{1+3+3}{10}=\frac{7}{10}$$
Assuming I wear colored or striped socks in first day, the probability of wearing colored or striped socks in second day is
$$\frac{1+3+3-1}{10-1}=\frac{6}{9}$$ 
Assuming I wear colored or striped socks in first and second day, the probability of wearing colored or striped socks in thirdday is
$$\frac{1+3+3-2}{10-2}=\frac{5}{8}$$
So, the answer is
$$\frac{7}{10}*\frac{6}{9}*\frac{5}{8}$$
