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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 :

MrRoyalidn

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]

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