Mathematics · Permutations and Combinations

JEE Main 2025 — 23 January, Evening Shift — Question 21

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

Numerical answer — enter this value.

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 $=5!\times 5!+4!\times 5!=17280$

Answer key and solution verified before publishing.

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