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,
[tex]\begin{gathered} ^nC_r=^9C_5 \\ =\frac{9!}{5!\times(9-5)!} \\ =\frac{9!}{5!\times4!} \\ =126 \end{gathered}[/tex]Thus, there are 126 ways of selecting 5 factories.
