Suppose fifteen people pick a number in the range {1,2,...,100}. Suppose each person picks independently and is equally likely to pick each number.

Suppose the first k people chose distinct numbers (that is none of them chose the same number), what is the probability the (k+1)st person chose a number different than any of the previous people

From this, find an expression for the probability that all 15 people chose distinct numbers and evaluate it numerically