The instructor in a writing seminar does not have time to gr

The instructor in a writing seminar does not have time to grade the seven essays submitted by his students. He decides to use a random-number generator to assign each essay a grade from 83 through 100, inclusive. What is the probability that at least two students will receive the same grade? The probability that at least two of the seven students will receive the same grade is

Solution

total essays = 7

probability that atleast 2 have same grades = 1 - probability 1 does not have same grade

probability that atleast 2 have same grades = 1 - {18 P 7 / 18^7 }

= 18 P 7 = 160392960

probability = 1- .26198 = .7380