Lời giải chi tiết:

\(C_x^0 + C_x^{x - 1} + C_x^{x - 2} = 79\)\(\left( {x \ge 0;\,\,\,x \in N} \right)\)

\( \Leftrightarrow \dfrac{{x!}}{{0!\left( {x - 0} \right)!}} + \dfrac{{x!}}{{\left( {x - 1} \right)!.1!}} + \dfrac{{x!}}{{\left( {x - 2} \right)!.2!}} = 79\)

\( \Leftrightarrow 1 + x + \dfrac{{\left( {x - 1} \right).x}}{{1.2}} = 79\)

\( \Leftrightarrow 2 + 2x + {x^2} - x = 158\)

\( \Leftrightarrow {x^2} + x - 156 = 0\)

\( \Leftrightarrow \left[ \begin{array}{l}x = 12\,\,\,\,\,\,\left( {tm} \right)\\x =  - 13\,\,\left( {ktm} \right)\end{array} \right.\) .

Chọn D.