What is the minimum number of people who would have to be enrolled in a school to guarantee that there were at least two students who have the same birthday (excluding year) and the same last initial ?
A) 9,909
B) 9,516
C) 9,490
D) 9,517
E) 9,491

Question

Quizplus · Accepted Answer

To guarantee that at least two students have the same birthday and the same last initial, we need to consider the maximum number of unique combinations of birthdays and last initials before a repeat is guaranteed. There are 365 possible birthdays (excluding leap years) and 26 possible last initials. Multiplying these gives 365 * 26 = 9,490 unique combinations. To guarantee a repeat, we need to add one more person, resulting in 9,491. However, the closest answer choice that is higher than 9,491 is 9,517.

What Is the Minimum Number of People Who Would Have