Pigeonhole Principle Statements
CMAT 2023 · Quantitative Techniques & Data Interpretation · Medium · Permutation and Combination
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:
- A.
Both Statement I and Statement II are correct
- B.
Both Statement I and Statement II are incorrect
- C.
Statement I is correct but Statement II is incorrect
- D.
Statement I is incorrect but Statement II is correct
A
Explanation
Statement I: Since there are 2 colors, by Pigeonhole Principle, drawing 3 masks guarantees at least 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 students. Adding 1 more student ensures at least 6 birthdays fall in the same month. So minimum students needed . Statement II is correct.
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