Answer
$100_{{C}{_{18}}}$ = 3.06 $\times10^{19}$
Work Step by Step
TOTAL NUMBER OF U.S SENATE MEMBERS = 100
NUMBER OF SENATE MEMBERS SERVING ON THE FOREIGN RELATIONS COMMITTEE = 18
THE NUMBER OF WAYS OF SELECTING 18 SENATE MEMBERS OUT OF 100= $100_{{C}{_{18}}}$
= $\frac{100!}{(100 - 18)! 18!}$
= $\frac{100!}{82!. 18!}$
= $\frac{100\times99\times98\times97\times96\times95\times94\times93\times92\times91\times90\times89\times88\times87\times86\times85\times84\times83\times82!}{ 82!.18\times17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}$
= $\frac{100\times99\times98\times97\times96\times95\times94\times93\times92\times91\times90\times89\times88\times87\times86\times85\times84\times83}{18\times17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}$
= 3.06 $\times10^{19}$
