A certain box has 8 cards and each card has one of the integers from 1 to 8 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 8 cards? Choose the correct choice from the following options
A) 1/8 B) 1/12 C) 1/14 D) 1/18 E) 1/28
The average of the numbers is 4.5   The total number of ways to choose 2 cards from 8 cards is 8C2 = 28.   The ways to choose 2 cards with a sum less than the average are: {1,2},{1,3}   The probability is 2/28 = 1/14   The answer is 1/14.
<result>C</result>
A certain box has 8 cards and each card has one of the integers from 1 to 8 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 8 cards?