Verified Solution • 2025–26 Session moderate

QJEEM25Mae829: JEE Main 2025 Mathematics - Class 11 JEEM25Mae829 Solution: The number of ways, 5 boys and 4 girls can sit in a row so that …

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 ________.

Step-by-Step Verified Solution

A : number of ways that all boys sit together =5!×5!=5!\times 5!

B : number of ways if no 2 boys

sit together =4!×5!=4!\times 5!

A∩B=ϕ\mathrm{A} \cap \mathrm{B}=\phi

Required no. of ways =5!×5!+4!×5!=17280=5!\times 5!+4!\times 5!=17280

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