2000 SMT/Advanced Topics Problems/Problem 4
Problem
Five positive integers from to are chosen without replacement. What is the probability that their sum is divisible by
Solution
The possibilities for the numbers are:
all five are divisible by three are divisible by one is and one is two are divisible by and the other three are either or one is divisible by two are and two are four are and one is four are and one is
This gives us possible combinations out of or . So, the probability is
Credit
Problem and solution were taken from https://sumo.stanford.edu/old/smt/2000/