<p>Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her is <em>[JEE Advanced 2014]</em></p>
Step-by-Step Solution
Key Concept: Count valid arrangements where every girl has strictly more boys than girls ahead. This is a ballot problem -- result is 1/2 by symmetry.
<p>Total arrangements: \(\binom{5}{2} = 10\) (choose positions for 2 girls).</p><p>Valid arrangements (boys ahead of each girl exceed girls ahead): by the ballot problem, exactly half the arrangements satisfy this condition.</p><p>Favorable = 5 arrangements. \(P = \dfrac{5}{10} = \dfrac{1}{2}\)</p>
Correct Answer: A