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Vera has $10$ white socks, $10$ black socks, $10$ brown socks, $10$ blue socks, and $10$ red socks. How many socks (at a minimum) must she pull out of her sock drawer to ensure at least two pairs of matching socks

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facundo3141592

The minimum number of socks that she needs to get such that a pair is always formed is 5.

How many socks must she get to be ensured of having a pair?

We know that she has:

  • 10 white socks.
  • 10 black socks
  • 10 brown socks
  • 10 blue socks.

First, we need to compute the maximum number of socks she needs to take in such a case that no pair is formed.

That will be 4, and represents the case where:

1 white sock, 1 black sock, 1 brown sock, and 1 blue sock are drawn. At that point, no pairs are formed.

Now, if she draws another sock, a pair will always be formed.

From this, we conclude that if she draws 5 socks, always at least one pair will be formed.

If you want to learn more about combinations, you can read:

https://brainly.com/question/11732255

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