Question

A math teacher randomly assigns seats in the classroom to students each quarter. Each student randomly chooses their row number out of a hat. In the classroom, there are 4 desks in each row and 27 students in your class. What is the probability that you and your 3 friends will get to sit together in the same row?

Answer 1

Using the combination formula, it is found that the probability that you and your 3 friends will get to sit together in the same row is given by:

$p = \frac{1}{17550}$.

We do not consider the order, hence the combination formula is used to solve this question.

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

4 students will be taken from a set of 27, hence the number of ways they can sit is given by:

$C_{27,4} = \frac{27!}{4!23!} = 17550$

Only one outcome is desired, hence the probability is given by:

$p = \frac{1}{17550}$.

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

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