Tính giá trị biểu thức (A49^12+A49^11)/A49^10-(A17^10+A17^9)/A17^8

Đáp án:

$1440$

Giải thích các bước giải:

\[\begin{array}{l}
\dfrac{{A_{49}^{12} + A_{49}^{11}}}{{A_{49}^{10}}} - \dfrac{{A_{17}^{10} + A_{17}^9}}{{A_{17}^8}}\\
 = \dfrac{{\dfrac{{49!}}{{\left( {49 - 12} \right)!}} + \dfrac{{49!}}{{\left( {49 - 11} \right)!}}}}{{\dfrac{{49!}}{{\left( {49 - 10} \right)!}}}} - \dfrac{{\dfrac{{17!}}{{\left( {17 - 10} \right)!}} + \dfrac{{17!}}{{\left( {17 - 9} \right)!}}}}{{\dfrac{{17!}}{{\left( {17 - 8} \right)!}}}}\\
 = \dfrac{{\dfrac{{49!}}{{37!}} + \dfrac{{49!}}{{38!}}}}{{\dfrac{{49!}}{{39!}}}} - \dfrac{{\dfrac{{17!}}{{7!}} + \dfrac{{17!}}{{8!}}}}{{\dfrac{{17!}}{{9!}}}} = \dfrac{{\dfrac{{49!}}{{37!}}\left( {1 + \dfrac{1}{{38}}} \right)}}{{\dfrac{1}{{39.38}}.\dfrac{{49!}}{{37!}}}} - \dfrac{{\dfrac{{17!}}{{7!}}\left( {1 + \dfrac{1}{8}} \right)}}{{\dfrac{1}{{9.8}}.\dfrac{{17!}}{{7!}}}}\\
 = \dfrac{{39}}{{38}}.\dfrac{{39.38}}{1} - \dfrac{9}{8}.\dfrac{{8.9}}{1} = 39.39 - 9.9 = 1440
\end{array}\]