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A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 9faculty members and 12 students eligible to serve on the committee. In how many ways can the committee be formed?

Respuesta :

[tex]\begin{gathered} The\text{ number of ways of selecting 4 faculty members from 9 faculty members is:} \\ 9C4=\frac{9!}{(9-4)!4!} \\ 9C4=\frac{9\times8\times7\times6\times5!}{5!\times4!} \\ 9C4=\frac{9\times8\times7\times6}{4\times3\times2\times1} \\ 9C4=\frac{3024}{24} \\ 9C4=126\text{ways} \end{gathered}[/tex]

The number of ways of selecting 5 students from 12 students is:

[tex]\begin{gathered} 12C5=\frac{12!}{(12-5)!5!} \\ 12C5=\frac{12\times11\times10\times9\times8\times7!}{7!\times5!} \\ 12C5=\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1} \\ 12C5=\frac{95040}{120} \\ 12C5=792\text{ways} \end{gathered}[/tex]

Hence, the number of ways of forming the committee is 126 x 792 = 99792 ways.

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