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Question

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 mn is

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Solution

Case:1n=5!×6!

where 5!=arranging of five girls

and 6!=arranging of five boys and five consecutive girls
Case:2
__ B __ B __ B __ B __ B __
m=5!× 5C4×4!× 6C2×2!
where 5!=arranging of five boys,
5C4=selecting of four girls,\
4!=arranging of four girls,
6C2=selecting two gaps in between five boys,
and 2!=arranging of four consecutive girls and one single girl
mn=5!× 5C4×4!× 6C2×2!5!×6!=5


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