SOLUTION: Here is the question: In how many ways can John, Todd, Lisa, and Marie line up so that they alternate gender? Here is the solution that I came up with (Choices for gender)

Question 204215: Here is the question:
In how many ways can John, Todd, Lisa, and Marie line up so that they alternate gender?
Here is the solution that I came up with
(Choices for gender)*(Number of ways to arrange the genders)

There two choices for gender: either a girl or a boy.
For the first position you can choose two boys, in the second you can choose two girls, in the third you can choose one boy, and in the fourth you can choose one girl:
Here it is:
2 * 2*1*2*1 = 8 ways of arranging them so that the genders are always alternated.
Please let me know if my reasoning is correct.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You have the correct answer, but either your reasoning is a little skewed or I'm having trouble understanding what you are saying. Look at it my way and see if it makes sense to you:

The first person in line can be any one of 4 people, so 4 ways to pick the first person. Once you have chosen the first person, the gender of the second person is fixed, and there are only 2 ways to pick the second person. There is then only 1 possibility left for the third person, and only 1 possibility for the fourth person. So:

John

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