A certain box has 9 cards and each card has one of the integers from 1 to 9 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 9 cards? Choose the correct choice from the following answers:
A) 1/36 B) 1/15 C) 1/18 D) 1/9 E) 2/9
The average of the numbers is 5.   The total number of ways to choose 2 cards from 9 cards is 9C2 = 36.   The ways to choose 2 cards with a sum less than the average are: {1,2},{1,3}   The probability is 2/36 = 1/18   The answer is 1/18.
<result>C</result>
A certain box has 9 cards and each card has one of the integers from 1 to 9 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 9 cards?