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There are 20 socks in a drawer: 5 pairs of black, 3 pairs of brown, and 2 pairs of white. You select the socks in the dark and can check them only after a selection has been made. What is the smallest number of socks you need to select to guarantee you get the following: At least one matching pair. At least one matching pair of each color.

Answer :

nekumaker2

Answer:

a 1:10 ratio

Step-by-step explanation:

francocanacari

At least one matching pair: 4 socks. At least one matching pair of each color: 18 socks.

Since there are 20 socks in a drawer: 5 pairs of black, 3 pairs of brown, and 2 pairs of white, and you select the socks in the dark and can check them only after a selection has been made, to determine what is the smallest number of socks you need to select to guarantee at least one matching pair, and at least one matching pair of each color, the following logical reasonings must be performed:

  • To guarantee at least one matching pair, 1 sock of each color must be chosen, with which the following sock will necessarily coincide with one of the previously chosen colors. Thus, since there are 3 colors, at least 4 socks must be selected to guarantee at least one matching pair.
  • In turn, to choose at least one matching pair of each color, following the same reasoning, knowing that there are 5 black pairs and 3 white pairs, the number of means that would guarantee a pair of each color would be 18 (5 x 2 + 3 x 2 + 2).

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