Thread: 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

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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4 ways ---------------answer.

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: . possible selections.


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

There are: . ways to choose all Accountants (no Mathematicians).


Therefore, there are: . ways that have at least one Mathematician.