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The owner of Brookstone coffee has 13 regular full-time employees. 7 are female and 6 are male. As he plans the schedule, he likes to ensure exactly two employees on any given shift are male. If 5 work a shift, how many combinations can be created?

Sagot :

Using the combination formula, it is found that 525 combinations can be created.

The order in which the employees 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:

  • 3 female employees are chosen from a set of 7.
  • 2 male employees are chosen from a set of 6.

Then the number of combinations is given by:

[tex]n = C_{7,3}C_{6,2} = \frac{7!}{3!4!} \times \frac{6!}{2!4!} = 525[/tex]

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

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