SOLUTION: Stephen has four blue socks and six gray socks in a drawer. What is the least number of socks he must select, at random, to guarantee having at least two socks of the same color?

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Question 246048: Stephen has four blue socks and six gray socks in a drawer. What is the least number of socks he must select, at random, to guarantee having at least two socks of the same color?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
4 blue
6 gray
wants to guarantee 2 socks with the same color.

I would have to say 3 socks minimum.

The possible number of sets of 2 socks each are 2^2 = 4

They are:

bb
bg
gb
gg

While some of these sets get 2 socks of the same color, not all of them do, so there is no guarantee.

The possible number of sets for taking 3 socks are 2^3 = 8.

They are:

bbb
bbg
bgb
bgg
gbb
gbg
ggb
ggg

All of these sets have at least 2 socks that are the same color.