The sixteenth day before the day fixed for the holding of the election of delegates shall be the last day for the filing of nominating petitions with the Department or, if such sixteenth day falls upon a Sunday or a legal holiday, the day following shall be the last day for the filing of such nominating petitions, and thereafter nominations for the office of delegate to such convention shall be closed. After the closing of such nominations, the Department shall forthwith count and determine the number of signatures which each candidate for nomination as delegate to such convention has obtained upon the candidate's or the Department's nominating petition or petitions. In making such count and determination, the Department shall only count the signatures of those persons who are qualified voters of the county which the candidates propose to represent at such convention. A signature to such nominating petition shall be prima facie evidence that the person purporting to sign the same did actually sign the same and that such person is a qualified voter of the same county as the county of residence of the candidate or candidates whose names appear in such nominating petition, and all signatures to such nominating petitions shall be counted by the Department, unless, within 5 days after the closing of nominations, evidence satisfactory to the Department shall have been produced before him or her that a person whose name purports to have been signed to a nominating petition is either a fictitious person or not a qualified voter of the county of residence of the candidate or candidates whose nominating petition the person purports to have signed. After the closing of nominations all nominating petitions shall be open to the inspection of any qualified voter of the county in which such petitions have been filed.