Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of \frac{m}{n} is

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Permutation and Combination Basic Definitions

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Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is

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n = number of ways in which all girls are consecutive = 6! · 5!

m = number of ways in which exactly 4 girls are consecutive = 5C4 × 5! × 6C2 × 2! × 4!

$∴ = \frac{m}{n} = \frac{^{5} C_{4} \cdot 5! \cdot^{6} C_{2} \cdot 2! \cdot 4!}{6! \cdot 5!} = 5 .$