Question

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?

Answer 1

Answer:

$Pr = \frac{1}{2002}$

Step-by-step explanation:

See comment for complete question;

Given

$n = 14$

$r = 5$ -- committee members

$k = 4$ ---- 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:

$^{14}C_5$

This gives:

$^{14}C_5 = \frac{14!}{9!5!}$

So, we have:

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

$^{14}C_5 = \frac{14*13*12*11*10}{5*4*3*2*1}$

$^{14}C_5 = \frac{240240}{120}$

$^{14}C_5 = 2002$

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

$Pr = \frac{1}{2002}$