Q:

Find the probability that the sum of the numbers in at least one horizontal row is greater than $21$.

Nine numbers $1,2,3, \ldots, 9$ are arranged in a rectangular array of matrix of order $3$ so that each number occurs exactly once.   Find the probability that the sum of the numbers in atleast one horizontal row is greater than $21$.
I counted the probability as $\frac{18+18+18}{9!}$ but the correct answer is $\frac{1}{7}$.  Can you please help me with correct approach to solve this? 

A:

Hints:

Show that a row with sum greater than $21$ must contain $9$
Count how many possibilities there are for the other two values in the row containing $9$
Count how many of those have a sum greater than $21$
Divide

