This problem is same as solving the below problem
Find total number of possible solution for given equation:
$x_1 + x_2+ x_2 = 12$
$x_i \geq 3, for\ i=1,2,3$
(Can be seen as number of ways to distribute 12 indistinguishable balls into 3 distinguishable bins, where each bin gets atleast 3 balls)
lets first put 3 in every box,
In total 3*3 = 9 numbers are gone
so above problem then further can be converted into:
number of ways to distribute 3 indistinguishable balls into 3 distinguishable bins, where each bin gets zero or more balls
$x_1 + x_2+ x_2 = 3$
$x_i \geq 0, for\ i=1,2,3$
soltuion to this problem is straight forward:
$\binom{3+3 -1}{3} = \binom{5}{3} = \binom{5}{2} = 10$ ways.