Question

Given below are two statements:

Statement I: A bag contains 10 white and 10 red face masks which are all mixed up. The fewest number of face masks you can take from a bag without looking and be sure to get a pair of the same color is 3.

Statement II: The minimum number of students needed in a class to guarantee that there are at least 6 students whose birthdays fall in the same month, is 61.

In the light of the above statements, choose the most appropriate answer from the option given below:

Accepted Answer

A. Statement I: Since there are 2 colors, by Pigeonhole Principle, drawing 3 masks guarantees at least $2$ masks of the same color. Thus, Statement I is correct. Statement II: To ensure at least 6 students share a birthday month, consider worst case where 5 students are born in each of the 12 months, totaling $5 	imes 12 = 60$ students. Adding 1 more student ensures at least 6 birthdays fall in the same month. So minimum students needed $= 60 + 1 = 61$. Statement II is correct.

Pigeonhole Principle Statements

Explanation

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