Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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?

Sagot :

[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.

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.