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Ten friends want to play a game. They must be divided into three teams with three people in each team and one field judge. In how many ways can they do it?

Respuesta :

Using the combination formula, it is found that there are 16,800 ways for them to do it.

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 have that:

  • For the judge, one is taken from a set of 10.
  • For the first team, 3 are taken from a set of 9.
  • For the second team, 3 are taken from a set of 6.
  • For the third team, 3 are taken from a set of 3.

Hence the number of ways is:

[tex]N = C_{10,1}C_{9,3}C_{6,3}C_{3,3} = \frac{10!}{1!9!} \times \frac{9!}{3!6!} \times \frac{6!}{3!3!} \times \frac{3!}{3!0!} = 16800[/tex]

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

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