The total number of non-negative integral solutions of $x_1+x_2+x_3+x_4=100$ is 

SOLUTION Here, the upper limit for the variables $x_1,x_2,x_3$ is more than 100 and the lower limit is non-negative. Therefore, required number of solutions 

= Coefficient of $x^{100}\mathrm{in}{\left(1+x+x^2+x^3+\dots \right)}^4$

= Coefficient of $x^{100}\text{ in }(1-x{)}^{-4}$

${=}^{100+4-1}{C}_{4-1}{=}^{100}{C}_3$