# Birthday Problem: Finding the Probability Three People Have the Same Birthday

all. I'm working on the following probability problem.

Birthday problems: 50 randomly selected students end up in a class, 365 days in a year. Find P for the following events.

-i- A is the event that 3 randomly chosen students have the same birthday.

-ii- B is the event that the tallest, second and third tallest student in the class each has the same birthday (assume no two people in the class are of exactly the same height).

-iii- C is the event that the tallest, second and third tallest student in the class each has a different birthday (assume no two people in the class are of exactly the same height).

-iv- No one in the class was born in the month of August.

-v- Every person in the class was born in one of the four Fall months (September through December).

I'm a little confused about parts (ii) and (iii). For problem (i), I understand that $$|\Omega|= 365^3 \, \Rightarrow P(A) = 1-\frac{365*364*363}{365^3} =0.0084$$ But for parts (ii) and (iii), I don't quite understand how to incorporate the sizes of each individual. Do their sizes matter, or can I just treat this problem the same I would for part (i)?

Thanks!

• The answer to the first part should be $365\times\frac{1}{365^3}$ Commented Jan 28, 2018 at 22:56
• what you have for (i) is the probability that the birthdays of three random students are not all different
– WW1
Commented Jan 28, 2018 at 23:16