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 2 or greater? Express your answer as a common fraction.

Lightning
Mar 18, 2018

#1**+2 **

There are: 7C2 =21 2-number combinations.

There are: 12, 23, 34, 45, 56, 67, or 6 combinations where the difference between them is < 2

21 - 6 = 15 combinations where the difference between them is 2 or > 2

15 / 21 = 5/7 probability that the difference between 2 randomly drawn numbers will be 2 or greater.

Guest Mar 18, 2018

#2**0 **

There are: 12, 23, 34, 45, 56, 67, or 6 combinations where the difference between them is < 2

21 - 6 = 15 combinations where the difference between them is 2 or > 2

15 / 21 = 5/7 probability that the difference between 2 randomly drawn numbers will be 2 or greater.

clement2017
Mar 18, 2018