The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ______ -

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] All boys together: treat them as one block with the 4 girls, $5!$ arrangements, times $5!$ inside the block $=14400$. No two boys together: arrange the girls in $4!$ ways, choose and order $5$ of the $5$ gaps: $4!\cdot5!=2880$. The two cases cannot overlap (5 boys cannot be both adjacent and separated). Total $=14400+2880=17280$. Answer: 17280.

Q. The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ______ -

Explanation

Reviewed by Dr. Abubacker

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