Question

Suppose n balls are distributed in n boxes. (i) what is the probability that exactly one box is empty? (ii) given that box 1 is empty, what is the probability that only one box is empty? (iii) given that only one box is empty, what is the probability that box 1 is empty?

Answer 1

Answer:

Let A be the empty box, and B be the box containing 2 balls and C is n−2 boxes containing 1 ball. So, there are 2(n2) ways of arranging the letter sequence ABC.....C. Then the size of the sample is (n+n−1n) because it is equivalent to the number of ways of placing n 0's and n−1 1's in the order. So the probability is n(n−1)(2n−1n)