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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 ?___

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Solution

Here, __B1 __B2 __ B3 __B4 __B5 __
Out of 5 girls, 4 girls are together and 1 girl is separate. Now,
no of ways to select 2 positions out of 6 positions between boys = 6C2 ...(i)
4 girls are to be selected out of 5 = 5C4 ways …(ii)
Now, 2 groups of girls can be arranged in 2! ways. …(iii)
Also, the group of 4 girls and 5 boys is arranged in 4!×5!ways ...(iv)
Now, total number of ways =6C2×5C4×2!×4!×5! [from Eqs. (i), (ii), (iii) and (iv)]
m=6C2×5C4×2!×4!×5!And n=5!×6!mn=6C2×5C4×2!×4!×5!6!×5!=15×5×2×4!6×5×4!=5

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