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.

Guest Jul 31, 2022

#1**0 **

There are \({7 \choose 2} = 21 \) choices

The only cases that work are (1, 4), (1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7), (3, 6), (3, 7), (4, 7)

So, the probability is \({9 \over 21} = \color{brown}\boxed{3 \over 7}\)

BuilderBoi Jul 31, 2022