Two different numbers are selected simultaneously and at random from the set {1,2,3,4,5,6,7}. What is the probability that the positive difference between the two numbers is 3 or greater? Express your answer as a common fraction.

There are: 7 nCr 2 = 21 differences as follows:

(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6)>>Total = 21

Simply count all the numbers from 3 and up and divide the total by 21, and that would be the probability.