# Find the number of ways in which 5 boys and 5 girls be seated in a row so that 1) No 2 girls mays sit together 2) All girls sit together and all boys sit together.3) all girls never sit together.

Hi!

Number of boys = 5
Number of girls = 5

(2)

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

(3)

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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