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A company is selecting 6 people to be on a committee. There are 29 employees eligible to be on the committee. What is the total number of ways the committee may be formed if the employees are selected at random and each employee will have a different position on the committee? (One person will be president, another vice president, ...) rstudio

Respuesta :

Answer:

There are 342,014,140 different ways that the committee can be formed.

Step-by-step explanation:

We can look at each position:

P1 - P2 - P3 - P4 - P5 - P6

P1 is the number of people that can be chosen for the first job, P2 for the second job, and so on...

For P1, any of the 29 employees may be selected.

For P2, any of them, other than the one at P1, can be chosen, so 28.

For P3, any of them, other than the ones at P1 and P2, can be chosen,so 27

And so on until P6.

So

29 - 28 - 27 - 26 - 25 - 24

The total number is:

[tex]T = 29*28*27*26*25*24 = 342,014,140[/tex]

There are 342,014,140 different ways that the committee can be formed.

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