Question
5 boys and 3 girls are to be seated on chairs arranged in a
row. If the arrangement is made at random, find the probability that no two girls will be seated next to one another.Solution
8 people can be seated on 8 chairs in 8! ways.
No two girls will be seated next to one another, so the arrangement would be like:
__ B __ B __ B __ B __ B __
5 boys can be seated at 5 places in 5! Ways. After this, 3 girls can be seated in the remaining 6 places in 6 P 3  ways.
Favorable outcomes= 5! XÂ 6 P 3 .
Probability = (5! x 6!)/(3! x 8!) = 5/14
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