California's population of 25 million proves that at least four people have the same first three letters and the same birthday (discrete math topic)

According to the most basic situation, the letters are 26 English letters, and a year is 365 days. According to probability theory,

The probability that a letter is the same is 1/26.

The probability that the first three letters are the same is (1/26) * (1/26) * (1/26).

The probability of the same Amanome is 1/365.

Therefore, the probability that the first three letters of the name are the same and the birthday is the same is (1/26) 3 * (1/365).

California has a population of 25 million.

The number of people with the same first three letters and the same birthday is

2500000000 * (1/26) 3 * (1/365) is approximately equal to 4.