Question

Evaluate the expression ${}^{5}C_2$?

Answer 1

Evaluate ${}^{5}C_2$

To evaluate ${}^{5}C_2$,use the following formula:

${}^{n}C_r=\frac{n!}{r!(n-r)!}$

Substitute $n=5\mathrm{and}r=2$ in above formula:

$$\begin{gathered} \therefore {}^{5}C_2=\frac{5!}{2!(5-2)!} \\ \Rightarrow {}^{5}C_2=\frac{5\times 4\times 3!}{2!\times 3!} \\ \Rightarrow {}^{5}C_2=\frac{20}{2} \\ \Rightarrow {}^{5}C_2=10 \end{gathered}$$

Hence, the value of ${}^{5}C_2$ is $10$.