A certain box has $10$ cards written integers from $1$ to $10$ inclusive and the numbers written are different.

A certain box has $10$ cards written integers from $1$ to $10$ inclusive and the numbers written are different. If $2$ different cards are selected at random, what is the probability that the sum of numbers written on the $2$ cards selected is less than the average (arithmetic mean) of total $10$ numbers written on the $10$ cards?

A. $2/45$
B. $1/15$
C. $4/45$
D. $1/9$
E. $2/15$

OA C

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