Rob has 10 white, 8 red, and 6 blue socks in his drawer. If he selects socks from the drawer randomly, without looking, what is the least number of socks Rob must select to guarantee that he has removed a pair of white socks?
Answer (3)
There is a total of 24 socks There are 10 white socks and 14 non white socks 24 15 Since there are 14 non white socks, he must pick 15 socks for one guarenteed white sock
Rob must select at least 15} socks to guarantee that he has removed a pair of white socks.
We need to consider the worst-case scenario where Rob avoids selecting a pair of white socks as long as possible.
Rob has:
10 white socks
8 red socks
6 blue socks
The worst-case scenario for avoiding a pair of white socks is to select all the red socks and blue socks first. Therefore, Rob could select all 8 red socks and all 6 blue socks without picking a pair of white socks.
After selecting all the red socks and blue socks, Rob would have:
8 red socks
6 blue socks
Total socks selected = 8 (red) + 6 (blue) = 14 socks.
Now, any additional sock selected must be a white sock because Rob has exhausted all the red and blue socks.
Therefore, to guarantee that Rob has selected at least one pair of white socks, he must select:
14 + 1 = 15
Rob must select at least 16 socks to guarantee that he has removed at least one pair of white socks. This number accounts for the worst-case scenario in which he picks all non-white socks first. By ensuring he picks 2 additional socks after selecting all non-white, he will secure a pair of white socks.
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