Chapter 11.7, Problem 54S

To determine

The value of the expression $C\left(5,2\right)$ .

Answer to Problem 54S

  $10$

Explanation of Solution

Given:

The expression $C\left(5,2\right)$ .

Formula used:

  $\begin{array}{l}C\left(n,r\right)=C{}_r=\frac{n!}{r!\cdot \left(n-r\right)!}\\ \text{where,}\\ n!=n\times \left(n-1\right)\times \left(n-2\right)\times \mathrm{...}\times 3\times 2\times 1\end{array}$

Calculation:

In order to evaluate the value of the given expression, use the above combination formula and simplify further as shown below,

  $\begin{array}{c}C\left(5,2\right)=C{}_2\\ =\frac{5!}{2!\cdot \left(5-2\right)!}\\ =\frac{5!}{2!\cdot 3!}\\ =\frac{5\cdot 4\cdot 3!}{2\cdot 1\cdot 3!}\\ =\frac{20}{2}\\ =10\end{array}$

Thus, the value of the expression is $10$.