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A software company employs 9 sales representatives and 8 technical representatives. How many ways can the company select 5 of these employees to send to a computer convention if at least 4 technical representatives must attend the convention?

Respuesta :

Using the combination formula, it is found that the company can select 5 of these employees in 686 ways.

The order in which the representatives are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, we can have:

  • 1 sales representative, from a set of 9, and 4 technical, from a set of 8.
  • 5 technical, from a set of 8.

Hence, the number of ways is given by:

[tex]N = C_{9,1}C_{8,4} + C_{8,5} = \frac{9!}{1!8!} \times \frac{8!}{4!4!} + \frac{8!}{5!3!} = 686[/tex]

More can be learned about the combination formula at https://brainly.com/question/25821700

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