Find the value of the combination \({^{12}C}_4\)

Concept:

We have the factorial representation of \({^{n}C}_r\) as, \(\frac{{n\;!}}{{r\;! \times \left( {n - r} \right)!}}\).

Calculation:

\({^{12}C}_4\) = \(\frac{{12\;!}}{{4\;! \times \left( {12 - 4} \right)!}}\)

\({^{12}C}_4\) = \(\frac{{12\;!}}{{4\;! \times \left( {8} \right)!}}\)

\({^{12}C}_4\) = \(\frac{{12 \times11 \times 10 \times 9}}{{4 \times 3 \times 2 \times 1}}\)

\({^{12}C}_4\) = 495

Hence the value of \({^{12}C}_4\) is 495.