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

`Pr = (1)/(2002)`

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 = (14!)/(9!5!)`

So, we have:

`^(14)C_5 = (14*13*12*11*10*9!)/(9!*5*4*3*2*1)`

`^(14)C_5 = (14*13*12*11*10)/(5*4*3*2*1)`

`^(14)C_5 = (240240)/(120)`

`^(14)C_5 = 2002`

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

`Pr = (1)/(2002)`