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Answer:
So the total number of ways in which the line-up can be made is 2880 ways.
Step-by-step explanation:
Please refer the attached figure for reference.
Now, there are 4 girls and 4 boys and we are asked to find the number of ways in which they can be lined up alternately.
That basically means that there should be a boy next to a girl in the arrangement.
So, at first we will arrange the 4 boys ( at B positions in the figure ), and that can be done in 4! ways.
Now, there are 5 positions ( 5 blue dots in the figure ), which can be taken by 4 girls, in such a way that the boys and girls are placed alternately.
So, 4 girls can take 5 positions in ways.
So the total number of ways in which the line-up can be made = 4! x = 24 x 120 = 2880 ways.
