Question

The Environmental Protection Agency must inspect 9 factories for complaints of water pollution. A representative can visit 5 of these factories this week 3. How many different groups of 5 factories are possible for this representative?

Answer 1

Given data:

The total numbers of factories are n=9.

The numbers of fctories selected are r=5.

The expression for selecting 5 factories is,

`\begin{gathered} ^nC_r=^9C_5 \\ =(9!)/(5!*(9-5)!) \\ =(9!)/(5!*4!) \\ =126 \end{gathered}`

Thus, there are 126 ways of selecting 5 factories.