A box contains 55 balls numbered from 1 to 55. If 8 balls are drawn with replacement, what is the probability that at least two of them have the same number?

Answer 1

Number of (ordered) ways to draw 8 balls with replacement
= 55^8
Number of ways to draw 8 different balls
=55P8
= 55!/47!

Probability of drawing 8 balls with at least two having the same number
= 1-(55!/47!)/55^8
= 25193936479/60897409375
= 0.414 approx.