## College Algebra (6th Edition)

$100_{{C}{_{18}}}$ = 3.06 $\times10^{19}$
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 $\times10^{19}$