A group of 8 boys and 6 girls are to stand in a straight line for a photograph. In how many ways can these 14 children be arranged so that none of the girls stand next to each other?

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A group of 8 boys and 6 girls are to stand in a straight line for a photograph. In how many ways can these 14 children be arranged so that none of the girls stand next to each other?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\( \large ^9P_6 \times 8! = \cdots \)
@FoolForMath how did you get that?
There are 9 places for 6 girls to go so that no girls would be together.

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Other answers:

2438553600
but there are only 7 places available so that the girls are not together
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two boys could be together too and yet the girls will be separated...
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