Answer
44,186,942,677,323,600 different committees.
Work Step by Step
The order in which the senators are selected is not important. It is a combination of 14 senators from a group of 100 senators.
$_{100}C_{14}=\frac{100!}{(100-14)!~14!}=\frac{100\times99\times98\times97\times96\times95\times94\times93\times92\times91\times90\times89\times88\times87\times86!}{86!~14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}=44,186,942,677,323,600$
