A certain box has 11 cards and each card has one of the integers from 1 to 11 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 11 cards?
Choose the correct answer
A) 1/11  B) 2/11  C) 2/33  D) 4/55  E) 5/66
The average of the numbers is 6   The total number of ways to choose 2 cards from 11 cards is 11C2 = 55.   The ways to choose 2 cards with a sum less than the average are:   {1,2},{1,3},{1,4},{2,3}   The probability is 4/55   The answer is 4/55.
<result>D</result>
A certain box has 11 cards and each card has one of the integers from 1 to 11 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 11 cards?