Given
The college is offering grants to 4 departments.
There are a total of 15 departments at the college.
To find the size of the sample space in this experiment.
Explanation:
It is given that,
The college is offering grants to 4 departments.
There are a total of 15 departments at the college.
Then, the size of the sample space in this experiment is,
[tex]\begin{gathered} Sample\text{ }size=nC_r \\ =15C_4 \\ =\frac{15!}{4!(15-4)!} \\ =\frac{15\times14\times13\times12\times11!}{(4\times3\times2)\times11!} \\ =\frac{15\times14\times13\times12}{12\times2} \\ =15\times13\times7 \\ =1365 \end{gathered}[/tex]Hence, the size of the sample space in this experiment is 1365.
