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JEE Advanced 2015 Mathematics question

MathematicsPermutations and CombinationsJEE Advanced 2015

Let 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 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 is

Answer: 5

Solution

: treat the 5 girls as one block: arrangements of (5 boys + block) and arrangements inside the block, so . : arrange the 5 boys in ways, creating 6 gaps. Choose and arrange the 4 girls forming the block in

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Question ID VK-026407