Answer
... of arrangements of 15 names, taken from a set of 20, in which "Hillary Clinton" is the 11th name.
Work Step by Step
The President is selecting 15 names (out of 20) with ORDER being important.
The first name chosen (person) will be the Secretary of Agriculture,
the second person will be Secretary of Commerce, and so on.
(It matters whether the name appears first or seventh on the list, because the Secretaries of Agriculture (1st) and Human Services (7th) are two different jobs.)
We are talking about arrangements, ordered lists.
So, S, the sample space ....
(a) ... is the set of arrangements of 15 names, taken from a set of 20, in which none of the names appears more than once.
