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!

Here is the answer to your question.

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 =

^{10}P_{10}= 10! ways.∴Total number of ways in which all the girls are never together = 10! – 5! 6! (Using (1))

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