Question

The Mathematics Department at VC has seventeachers. Four will be randomly selected toattend a Mathematics Conference. How manydifferent ways can the 4 be selected?

Answer 1

We have 7 teachers and we will select groups of 4.

We have to find how many ways we can select them.

As the order does not matter, this is a combination of 7 into 4.

We can then calculate it as:

`\begin{gathered} C(n,r)=(n!)/(r!(n-r)!) \\ C(7,4)=(7!)/(4!3!)=(5040)/(24*6)=(5040)/(144)=35 \end{gathered}`

Answer: we can select them in 35 different ways.