Permutations and Combinations
Block Method
JEE Advanced 2015 Paper 1
Grade 11
Question:
Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue such that all girls stand consecutively. Let $m$ be the number of ways in which all girls do not stand consecutively, with exactly $4$ girls standing consecutively. Then $m/n$ is _____.
Step-by-Step Solution
Key Concept: $n = 6! \times 5!$ (girls as a block: $6!$ for block+boys, $5!$ inside). For $m$: choose the 1 isolated girl (5 ways), arrange 4-girl block + 5 boys + 1 isolated girl as 7 units ($7!$ ways, $4!$ internal), subtract arrangements where isolated girl is adjacent to block ($2 \times 6! \times 4!$). $m/n = 5$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 5