Immediately upon the adoption of such form of government, the judge of probate of the county with whom the petition was filed shall call an election to be held under and to be governed by this part not less than 90 days nor more than 120 days after the date of such call, the expense thereof to be paid by such city, for the election at large of nine council members and a mayor by the qualified voters of such city. The nine candidates for the council receiving a majority of the votes cast in the election shall be elected to the council; and in the event that nine candidates should fail to receive such a majority, then and in that event those candidates for the council receiving a majority shall be elected, and another election shall be held upon the same day of the week four weeks thereafter to be called and held in the same mode and manner and under the same rules and regulations. In the second election there shall be two candidates for each place upon the council to be filled in such second election; and these candidates shall be the ones who received the highest number of votes but who were not elected at the first election. The candidate or candidates for the council receiving the highest number of votes cast in the second election shall be elected, so that in the first and second elections only nine council members shall be elected. The terms of office of such candidates so elected shall commence immediately upon their election and qualification. The four such council members so elected receiving the largest number of votes in the first election, if at least four council members are elected thereat, shall hold office until the second Tuesday in November of that year ending in an odd number which would give them a term of office most closely approximating four years and until their successors are elected and qualify. If four council members are not elected at the first election, then those who are elected at such second election and the council members receiving the highest vote at the second election sufficient to bring the total number of such council members to four, shall hold office as provided in the preceding sentence. The remaining five such council members so elected shall hold office until the second Tuesday in November of that year ending in an odd number which would give them a term of office most closely approximating two years and until their successors are elected and qualify. The candidate for mayor receiving the largest number of votes for the office at the first election thereto, provided such candidate receives a majority of all votes cast for such office. If at the first election no candidate received a majority of the votes cast for the office of mayor at such election, then another election shall be held upon the same day of the week four weeks thereafter to be called and held in the same mode and manner and under the same rules and regulations. In the second election there shall be two candidates for the office of mayor; and these candidates shall be the two who received the highest number of votes for the office at the first election. In the election of the first council and first mayor and all subsequent elections held under this part, no vote shall be permitted by writing in a person’s name on the ballot and, further, no name shall appear upon the ballot as a candidate for election except the names of such persons as have become candidates according to this part.