I was trying to solve the following problem:
$n$ boys and $n-1$ 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
This does resemble the types of problems of $n$ open braces, and $n$ closing braces solved using Catalan's number. However, I was not able to convert this into the same idea since here $n-1$ girls are present instead of $n$. And, I fear that if I calculate the permutations based on $n$ girls instead of $n-1$ the answer might turn to be different. So I'm not able to prove if they are equal. How should I proceed?