Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

appoint a planning committee with five different members. There are 14 qualified​ candidates, and officers can also serve on the committee. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified​ candidates?

Sagot :

MrRoyal

Answer:

[tex]Pr = \frac{1}{2002}[/tex]

Step-by-step explanation:

See comment for complete question;

Given

[tex]n = 14[/tex]

[tex]r = 5[/tex] -- committee members

[tex]k = 4[/tex] ---- officers (i.e. president, CEO, COO and CFO)

Required

Probability of selecting 5 youngest qualified members

First, we calculate the number of ways the committee can be appointed;

Any 5 members can be part of the committee; This means that we won't consider the order.

So, the number of ways is:

[tex]^{14}C_5[/tex]

This gives:

[tex]^{14}C_5 = \frac{14!}{9!5!}[/tex]

So, we have:

[tex]^{14}C_5 = \frac{14*13*12*11*10*9!}{9!*5*4*3*2*1}[/tex]

[tex]^{14}C_5 = \frac{14*13*12*11*10}{5*4*3*2*1}[/tex]

[tex]^{14}C_5 = \frac{240240}{120}[/tex]

[tex]^{14}C_5 = 2002[/tex]

There can only be a set of 5 young people. So, the probability is:

[tex]Pr = \frac{1}{2002}[/tex]

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.