How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 9 forwards, 7 midfield players, and 7 defensive players?

Respuesta :

Using the combination formula, it is found that there are 37,044 ways to form the soccer team.

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 forwards are taken from a set of 9.
  • 4 midfielders are taken from a set of 7.
  • 3 defenders are taken from a set of 7.

Since they are independent of each other, the total number of combinations is given by:

[tex]T = C_{9,3} \times C_{7,4} \times C_{7,3} = \frac{9!}{3!6!} \times \frac{7!}{3!4!} \times \frac{7!}{3!4!} = 37,044[/tex]

There are 37,044 ways to form the soccer team.

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

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