Combination probability problem of students picking crayons at random.

Question

I am having this problem at the Blaine WSMC competition 2018 test, and I still can't figure this out. The full problem is here:

A classroom of 27 students each have an identical box of 64 uniquely-colored crayons. One at a time, students choose one of their crayons at random. How many students must choose a crayon in order for there to be at least a 30% probability that there is a matching crayon?

Any help will be appreciated, thank you!

Answer 1

Hint: Find the probability of no matching crayons after 1 student has chosen. Then after two students have chosen. Then after three students have chosen. Keep going until you reach the desired probability.