JEE MAIN - Mathematics (2025 - 23rd January Evening Shift - No. 23)
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 ________.
Answer
17280
Explanation
A : number of ways that all boys sit together $=5!\times 5!$
B : number of ways if no 2 boys
sit together $=4!\times 5!$
$\mathrm{A} \cap \mathrm{B}=\phi$
Required no. of ways $=5!\times 5!+4!\times 5!=17280$
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