1. ## Work Woes

The executive director of the "smart solutions" company wishes to employ 9 new staff members. There are 14 applicants: 4 Mathemiticians and 10 accountants. In how many ways can the executive director select 9 people if he wants to employ atleast one mathematician?

Heroes Wanted

2. Originally Posted by googa
The executive director of the "smart solutions" company wishes to employ 9 new staff members. There are 14 applicants: 4 Mathemiticians and 10 accountants. In how many ways can the executive director select 9 people if he wants to employ atleast one mathematician?

Heroes Wanted
At least one Mathematician.

4M and 5A
3M and 6A
2M and 7A
1M and 8A
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3. Hello, googa!

The executive director of a company wishes to employ 9 new staff members.
There are 14 applicants: 4 Mathematicians and 10 Accountants.
In how many ways can the executive director select 9 people
if he wants to hire at least one Mathematician?
There are: . ${14\choose9} = 2002$ possible selections.

The opposite of "at least one Mathematician" is "no Mathematicians" (all Accountants).

There are: . ${10\choose9} = 10$ ways to choose all Accountants (no Mathematicians).

Therefore, there are: . $2002 - 10 \:=\:\boxed{1992}$ ways that have at least one Mathematician.