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Let n be the number of ways in which 5 b...

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 in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of `m/n` is ____

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The correct Answer is:
5
`n=5!xx6!`
For m: 5 boys can stand in a row in 5!, creating 6 alternate space for girls. A group of 4 girls can be selected in `.^(5)C_(4)` ways. A group of 4 and single girl can be arranged at 2 places out of 6 in `.^(6)P_(2)` ways. Also, 4 girls can arrange themselves in 4! ways.
`thereforem=5!xx.^(6)P_(2)xx.^(5)C_(4)xx4!=5!xx30xx5x4!=5!xx6!xx5`
`implies(m)/(n)=(5!xx6!xx5)/(5!xx6!)=5`
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