eligibility
Being allowed to do something because you meet the rules.
Eligibility means meeting the requirements or qualifications needed to do something, participate in something, or receive something. When you're eligible for something, you've satisfied all the conditions that allow you to take part.
Think of eligibility as passing through a checkpoint. Before you can try out for the basketball team, you might need to maintain good grades and have a permission slip signed. Those are the eligibility requirements. A student who meets them has eligibility to try out. Someone who doesn't meet them is ineligible.
Eligibility shows up everywhere in life. To get a library card, you need eligibility, which might mean living in the library's service area. To run for class president, you need eligibility, which might require a certain grade point average. Professional athletes carefully maintain their eligibility by following their sport's rules, because breaking those rules can make them ineligible to compete.
When you're eligible for something, you've made yourself eligible by meeting the standards. Eligibility doesn't guarantee you'll be selected or win, but it means you're qualified to be considered. Without it, the door stays closed before you even get a chance.