The number of the 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 __________. [2025]

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Solution

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 __________. [2025]

Ans.
(17280)

Number of ways that all boys sit together $= 5! \times 5!$

Number of ways no two boys sit together $= 4! \times 5!$

$∴$ Required number of ways $= 5! \times 5! + 4! \times 5! = 17280$

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