Question

If a student writes random strings of length 3 using the vowels (A,E,I,O,U) only, how many times is he required to write such strings to be sure that he has written a string twice?

Answer 1

Answer:  126

Reason

There are 5 vowels and 3 slots to fill. We have 5^3 = 125 different strings possible (repeat letters are allowed).

The student's goal is to randomly write the same string twice. That takes 2 attempts with the best luck possible.

But we have to consider the the worst luck possible. The worst luck situation is when the student writes all 125 strings without repeating any so far.

If the student writes all 125 strings out, then the 126th string is when they will land on another string already written. This is simply because there aren't any strings left. Formally this is known as the pigeon hole principle.