In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: 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 ? 
Options: a ) 1 / 11 , b ) 2 / 11 , c ) 2 / 33 , d ) 4 / 55 , e ) 5 / 66
d