In this work, we introduce the concept of Fermat’s Urn, an urn containing three types of marbles, and such that it holds a peculiar constraint therein: The probability to get at least one marble of a given type (while performing multiple independent drawings) is equal to the probability not to get any marble of another type. Further, we discuss a list of implicit hypotheses related to Fermat's Equation, which would allow us to interpret this equation exactly as the mentioned constraint in Fermat's Urn. Then, we study the properties of this constraint in relation with the capability to distinguish the types of marbles within the urn, namely in case of the event ''to get at least one marble of each type''. Eventually, on the basis of a simple theorem related to this event, we prove that Fermat's Equation and Fermat's Urn may share those properties only if we perform at most two drawings from the urn. This result reflects then in the solution of Fermat's Equation.