The number of distinct pairs of integers (x, y) satisfying the inequalities $$x>y\geq3 $$ and $$x+y<14$$ is

It is given, $$x>y\geq3 $$ and $$x+y<14$$

Now for $$y=3$$, the values of $$x$$ can be 4,5,6,7,8,9,10  (7 cases)

Then for $$y=4$$, the values of $$x$$ can be 5,6,7,8,9 (5 cases)

Then for $$y=5$$, the values of $$x$$ can be 6,7,8 (3 cases)

Then for $$y=6$$, the values of $$x$$ will be 7 (1 case)

So, total number of cases =1+3+5+7=16 cases