A certain box has 12 cards and each card has one of the integers from 1 to 12 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 12 cards? Choose the most appropriate option:
A) 1/11 B) 2/23 C) 3/34 D) 4/45 E) 5/56
The average of the numbers is 6.5   The total number of ways to choose 2 cards from 12 cards is 12C2 = 66.   The ways to choose 2 cards with a sum less than the average are:   {1,2},{1,3},{1,4},{1,5},{2,3},{2,4}   The probability is 6/66 = 1/11   The answer is 1/11.
<result>A</result>
A certain box has 12 cards and each card has one of the integers from 1 to 12 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 12 cards?