The value of ${ }^{50} \mathrm{C}_4+\sum_{\mathrm{r}=1}^6{ }^{56-\mathrm{r}} \mathrm{C}_3$ is

Question

Professor PC Thomas Classes · Answer

$ \begin{aligned} & { }^{50} \mathrm{C}_4+{ }^{50} \mathrm{C}_3+{ }^{51} \mathrm{C}_3+\ldots+{ }^{55} \mathrm{C}_3={ }^{56} \mathrm{C}_4 \ & 	ext { use }{ }^n \mathrm{C}_{\mathrm{r}}+{ }^n \mathrm{C}_{\mathrm{r}-1}={ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}} \end{aligned} $