The number of solutions of the equation \(x_1 + x_2 + x_3 + x_4 = 50\), where \(x_1, x_2, x_3, x_4\) are integers with \(x_1 \geq 1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0\) is

Question and options

The number of solutions of the equation

x_1 + x_2 + x_3 + x_4 = 50

, where

x_1, x_2, x_3, x_4

are integers with

x_1 \geq 1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0

Correct answer: C - 19600

Put y1=x1-1, y2=x2-2: y1+y2+x3+x4=47 with all >=0, count C(50,3)=19600.