# Binomial theorem counting number of solutions .

How to find the number of solutions to the equation $x_1 +x_2 +x_3 +x_4 +x_5 = 37$, where $x_1, x_2, x_3, x_4, x_5$ are non-negative integers, $x_2 ≥ 8, x_3 ≥ 7, x_4 ≥ 2$ and $x_5 < 4$.

Is this topic comes under binomial theorem

Hint: $x_5=0 \to x_1+(y_2+8)+(y_3+7)+(y_4+2) = 37$, and use Star-And-Bar method.
Do this to each $x_5 = 0,1,2,3$.