stilesm858 stilesm858

25-06-2024
Mathematics

Answered

Explain why in a drawer containing only two different colors of socks, one must draw only three socks to find a matching pair.

Choose the correct answer below.

A. If there are only two colors of socks in the drawer, then of any two chosen, both must be the same color.
B. If there are only two colors of socks in the drawer, then of any three chosen, two must be the same color.
C. Regardless of the number of different colors of socks in the drawer, one must only draw one more sock than the desired number of matching socks in order to get a matching set. Therefore, in order to get two matching socks, one must draw only three from the drawer.
D. It is not the case that one must draw only three socks to find a matching pair.

Answer :

GinnyAnswer GinnyAnswer

25-06-2024

Final answer:

In a drawer with two different colors of socks, drawing three socks guarantees a matching pair due to the Pigeonhole Principle.

Explanation:

The reason why one must draw only three socks to find a matching pair in a drawer containing two different colors of socks is because of the Pigeonhole Principle. With only two colors, drawing three socks guarantees at least two socks of the same color. For example, if there are red and blue socks, drawing three socks can result in either all red socks or two socks of the same color (red or blue).

Learn more about Probability and Combinatorics here:

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