@Yi52You have an interesting model: 10 guests allowed ($467 regardless how many show up) but only 4 adults allowed, unusual way to discourage parties. I wonder what is worse; 6 hgh-energy kids or a real party of 10 adults. Perhaps giving other ways a chance may serve you well.
Consider charging 'X" after 4 persons, this tends to discourage parties (they love the flat fee places; in this case $467/10 =$47 each). Maybe starting at $450 for 4 and $100 extra per couple after. This will encourage adults vs. children that are oftentimes tougher on places.
On this particular case, the fact they are just 24-32 years old and recently out of college begs the question: how many already own their own nice place to identify with your nice place?
The fact they were already coy on how many are indeed coming (and their age range) is suspect.
Best not think of exceptions (and yes I can think of many also), but of probability.