JEE Advanced 2015 · Paper 1 · Mathematics Q44

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MathematicsInteger+4Question 44 of 60

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 $\dfrac mn$ is

Your answer

Answer and worked solution

Official answer: 5

n: all girls together. Treat the girls as one block: $n=6!\,5!$ .

m: exactly four girls together.

Arrange the boys: $5!$ .
Choose the girl who stands apart (5 ways) and order the block of four ( $4!$ ).
Place the block and the single girl in two different gaps among the boys' 6 gaps, so they are not adjacent: $6\times5$ ways.

$m=5!\cdot5\cdot4!\cdot30.$

Ratio.
$\frac mn=\frac{5\cdot24\cdot30}{720}=5.$

Answer: 5

Topics:Permutations

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JEE Advanced 2015 · Paper 1, Mathematics question 44