Question

Four nonbinary and four trans people line up at a checkout counter in a store. in how many ways can they line up if the first person in line is nonbinary,​, and the people in line alternate nonbinary, trans, nonbinary, trans, and so on

Answer 1

There are 576 ways for four nonbinary and four trans people to line up at a checkout counter alternating starting with a nonbinary person, calculated as 4! multiplied by 4!.

Step-by-step explanation:

The student asked: In how many ways can four nonbinary and four trans people line up at a checkout counter in a store if the line must alternate starting with a nonbinary person?

To solve this, we recognize that the arrangement will be in the form NB-T-NB-T-NB-T-NB-T, where NB represents a nonbinary person and T represents a trans person.

Since the first person is nonbinary and they must alternate, there are 4! ways to arrange the nonbinary individuals and 4! ways to arrange the trans individuals. Thus, the total number of ways they can line up is:

4! × 4! = 24 × 24 = 576 ways.