Question

The value of ${}^{15}\mathrm{C}_3+{}^{15}{\mathrm{C}}_{13}$is?

• A. ${}^{16}{\mathrm{C}}_3$
• B. ${}^{30}{\mathrm{C}}_{16}$
• C. ${}^{15}\mathrm{C}_{10}$
• D. ${}^{15}\mathrm{C}_{15}$

Answer 1

The correct option is A

${}^{16}{\mathrm{C}}_3$

The explanation for the correct answer.

Given: ${}^{15}\mathrm{C}_3+{}^{15}{\mathrm{C}}_{13}$

$$\begin{gathered} {}^{15}{\mathrm{C}}_{13}={}^{15}{\mathrm{C}}_2\left[\because {}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}={}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{n}-\mathrm{r}}\right] \\ {}^{15}\mathrm{C}_3+{}^{15}{\mathrm{C}}_2={}^{16}{\mathrm{C}}_3\left[\because {}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}+{}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}-1}={}^{\mathrm{n}+1}{\mathrm{C}}_{\mathrm{r}}\right] \end{gathered}$$

Hence $o\mathrm{ption}\left(\mathrm{A}\right)$ is the correct answer.