Answer
$16,007,560,800$ different samples.
Work Step by Step
The order in which the objects from a population are selected does not matter and no object can be selected more than once.
Combination of 100 distinct objects taken 7 at a time:
$_{100}C_{7}=\frac{100!}{7!(100-7)!}=\frac{100!}{7!\times93!}$
But, $100!=100\times99\times98\times97\times96\times95\times94\times(93\times92\times91\times...\times3\times2\times1)=100\times99\times98\times97\times96\times95\times94\times93!$
$_{100}C_{7}=\frac{100\times99\times98\times97\times96\times95\times94\times93!}{7!\times93!}=\frac{100\times99\times98\times97\times96\times95\times94}{7\times6\times5\times4\times3\times2\times1}=16,007,560,800$
