When m balls are distributed into n bins uniformly at random, what is the probability that the first bin remains empty?

Question

Answer:  [(n − 1)/n]^m

Answer 1

In the favorable case we have (n-1) choices for each of the m balls and the total number of choices for each ball is m. So, probability

= [(n-1)/n]^m

[Here first bin is fixed. Had it been any one bin being empty, answer would have been multiplied by _nC₁]

Comments

Thanks.
Its all about the choice we have for each ball and multiply the choices.