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  4. 5 boys and 3 girls sit in a line so that p is the number of arrangements when no two girls sit together and q is the number of arrangements when all the girls sit together, then (p/q) is

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Q. 5 boys and 3 girls sit in a line so that $p$ is the number of arrangements when no two girls sit together and $q$ is the number of arrangements when all the girls sit together, then $\frac{p}{q}$ is

Permutations and Combinations

Solution:

$ p=5 !{ }^6 C _3 \cdot 3 !, q =6 ! \cdot 3 ! $
$\Rightarrow \frac{ p }{ q }=\frac{10}{3}$