Here is the answer to your question.
Number of boys = 5
Number of girls = 5
Two groups of 5 girls and 5 boys can be arranged in 2! ways.
5 girls can arrange among themselves in 5! ways.
5 boys can arrange among themselves in 5! ways.
Hence, total number of ways of seating arrangements = 2! × 5! × 5! = 2! × (5!)2
Total number of ways in which all the girls are never together = Total number of arrangements – Number of arrangement in which all the girls are always together.
Total number of arrangement of 5 boys and 5 girls = 10P10 = 10! ways.
∴Total number of ways in which all the girls are never together = 10! – 5! 6! (Using (1))
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