Question

A drawer contains 60 pairs of socks. Each pair is one of four colors. What is the minimum number of socks that must be drawn, at random, from the drawer to ensure that a pair of matching-color socks is selected? Plz help!

Answer 1

Minimum 5 socks needs to be selected.

Explanation:

Given that there are four different colors of socks.

So, if you pick 4 socks , in worst case it will be all four of different color.

now if you pick 5th socks it will be either of those four colors.

Hence, minimum 5 socks must be taken to ensure that a pair of matching-color socks is selected.

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To elaborate it more,

let four colors be red, yellow, blue , green

if you pick 5 socks, then in worst case four will be all of different color

red, yellow, blue , green but fifth will be

• If red socks, then there will 1 pair of red socks
• If yellow socks, then there will 1 pair of yellow socks
• If blue socks, then there will 1 pair of blue socks
• If green socks, then there will 1 pair of green socks

Hence. minimum 5 socks needs to be selected.

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In general, if you have n objects of different colors then you need to take minimum n+1 number of object to have at least two object of same color.