Alicia, Bill, and Ross are in Group A. David, Maddie, and Shelby are in Group B.The students are going to have their pictures taken. They will stand in 2 rows by group, and group members cannot be separated. If 2 girls or 2 boys cannot be standing next to each other, how many different ways can they a row?

To find the number of different ways the students can form a row, we need to consider the constraints given in the question.

First, let's consider the groups individually:

Group A: Alicia, Bill, and Ross
Group B: David, Maddie, and Shelby

Since group members cannot be separated, each group needs to be arranged within itself first, before arranging the groups together.

For Group A, there are 3 members. We can calculate the number of possible arrangements within this group using the factorial function, denoted by "!". So, the number of arrangements within Group A is 3!

Similarly, for Group B, where there are also 3 members, the number of arrangements within this group is also 3!.

Now, we need to consider the arrangement of the two groups.

Since group members cannot be standing next to members of the same gender, we need to ensure that there is always at least one person of the opposite gender between two individuals of the same gender.

Let's analyze the possibilities:

1. Starting with a boy: We can start with either David or Ross, but once we choose one, the following arrangement becomes fixed. The remaining two boys must be arranged in the two available spots, leaving one spot for the girl. So, for each boy chosen to start, there are 2! ways to arrange the two remaining boys and 1! way to arrange Alicia and Maddie. Therefore, there are 2! * 1! * 2! possible arrangements when starting with a boy.

2. Starting with a girl: Again, we can start with either Alicia or Maddie, but once we choose one, the following arrangement becomes fixed. The remaining two girls must be arranged in the two available spots, leaving one spot for the boy. So, for each girl chosen to start, there are 2! ways to arrange the two remaining girls and 1! way to arrange David and Ross. Therefore, there are 2! * 1! * 2! possible arrangements when starting with a girl.

Since we have two possibilities (starting with a boy or a girl) and each has a specific number of arrangements, we need to add these possibilities together to get the total number of arrangements.

Total number of arrangements = (2! * 1! * 2!) + (2! * 1! * 2!)

Simplifying this expression gives us:

Total number of arrangements = 2 * 1 * 2 + 2 * 1 * 2

Now we can calculate the total number of arrangements:

Total number of arrangements = 4 + 4 = 8

Therefore, there are 8 different ways they can form a row while following the given constraints.