Question

How many ways can 11 boys on a soccer team be grouped into 4 forwards, 3 midfielders, 3 defenders, and 1 goalie

Answer 1

Using arrangements with repetitions, it is found that they can be grouped in 46,200 ways.

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

$A_n = n!$

When elements are repeated $n_1, n_2, \cdots, n_n$ times, the formula is as follows:

$A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}$

In this problem:

• There are 11 boys, hence $n = 11$.

• They are divided into 4 forwards, 3 midfielders, 3 defenders, and 1 goalie, hence $n_1 = 4, n_2 = 3, n_3 = 3, n_4 = 1$.

Then, the number of ways they can be grouped is:

$A_{11}^{4,3,3,1} = \frac{11!}{4!3!3!1!} = 46200$

You can learn more about arrangements at https://brainly.com/question/24828983