Question

Evaluate the expression express your answer in exact simplest form12C3=

Answer 1

Given:

$_{12}C_3$

Find-: Evaluate the expression.

Sol:

Formula:

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

So the value is:

$_{12}C_3=\frac{12!}{3!(12-3)!}$$\begin{gathered} =\frac{12!}{3!(12-3)!} \\ \\ =\frac{12\times11\times10\times9!}{3!\times9!} \\ \\ =\frac{12\times11\times10}{3!} \end{gathered}$

value is:

$\begin{gathered} =\frac{12\times11\times10}{3!} \\ \\ =\frac{12\times11\times10}{3\times2\times1} \\ \\ =\frac{12\times11\times10}{6} \\ \\ =2\times11\times10 \\ \\ =22\times10 \\ \\ =220 \end{gathered}$

So the value is 220.