Question

combinari de 99 luate câte 10 plus combinari de 99 luate câte 9

Answer 1

$C_{99} ^{10}+C_{99}^{9}= \frac{99!}{89!*10!}+ \frac{99!}{90!*9!} =$
$\frac{99!}{89!*10!}+ \frac{99!}{90!*9!} |[tex] \frac{99!}{89!*10!}+ \frac{99!}{90!*9!}= \frac{99!}{89!} ( \frac{1}{10!} + \frac{1}{90*9!})= \frac{99!}{89!} ( \frac{1}{9!*10}+ \frac{1}{90*9!} )= \frac{99!}{89!}* \frac{10}{90*9!}$