Question

There are 13 students in a​ class: 8 are wearing all blue and 5 are wearing all green. The teacher assigns seats at random. How many distinguishable seating arrangements are possible if students are only distinguishable by the color they are​ wearing?

Answer 1

Using the arrangements formula, the number of distinct seating arrangements is:

1287.

What is the arrangements formula?

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

$A_n = n!$

When elements are divided and classified with repetition, the number of arrangements is given as follows:

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

In the context of this problem, the parameters are given as follows:

• n = 13, as there are 13 students in the class.

• $n_1 = 8$, as 8 of the students are wearing all blue.

• $n_2 = 5$, as 5 of the students are wearing all red.

Hence the number of distinct seating arrangements is calculated as follows:

$A_{13}^{8,5} = \frac{13!}{5!8!} = 1287$

More can be learned about the arrangements formula at brainly.com/question/20255195

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