Question

The college is offering grants to 4 departments.There are a total of 15 departments at thecollege. What is the size of the sample space inthis experiment?

Answer 1

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.

Step-by-step 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,

`\begin{gathered} Sample\text{ }size=nC_r \\ =15C_4 \\ =(15!)/(4!(15-4)!) \\ =(15*14*13*12*11!)/((4*3*2)*11!) \\ =(15*14*13*12)/(12*2) \\ =15*13*7 \\ =1365 \end{gathered}`

Hence, the size of the sample space in this experiment is 1365.