How many rental applications will you accept in a hot market?

[Denise B.]

I listed a townhome for rent in my very tight rental market on Monday and I've received well over 100 inquiries.  I've been responding via email/text with a link to my application and application requirements and the times for my open houses this coming weekend.  I'm getting a little concerned about the number of people that may show up.  In the past, I've received 20-50 inquiries and maybe 10 parties show up at the open house with 3-4 actually submitting an application.  I have no expectation that everyone will come but I do think there's potential for more than 5-10 applications to be submitted.  I have written requirements about income, credit score, etc so the applicants should be able to determine if they meet the base requirements on their own.  How many apps do you normally accept on a unit?  If you are running an open house, do you accept all applications offered during that open house or do you pause acceptance at some point to process the apps already received?