Answer
$\frac{10_{{C}{_{3}}}}{6_{{C}{_{4}}}}$ - $\frac{46!}{44!}$ = - 2062
Work Step by Step
$\frac{10_{{C}{_{3}}}}{6_{{C}{_{4}}}}$ - $\frac{46!}{44!}$
= $\frac{\frac{10!}{(10 - 3)!. 3!}}{\frac{6!}{(6 - 4)!.4!}}$ - $\frac{46!}{44!}$
= $\frac{\frac{10!}{7!. 3!}}{\frac{6!}{2!.4!}}$ - $\frac{46!}{44!}$
= $\frac{\frac{10\times9\times8\times7!}{7!. 3\times2\times1}}{\frac{6\times5\times4!}{2!.4!}}$ - $\frac{46\times45\times44!}{44!}$
= $\frac{\frac{10\times9\times8}{3\times2}}{\frac{6\times5}{2}}$ - $46\times45$
= $\frac{120}{15}$ - $46\times45$
= 8 - 2070
= - 2062