The mayor in the case of an authority of a city, or the governing body in the case of an authority of a county, shall designate which of the commissioners appointed must be the first chairman. When the office of the chairman of the authority thereafter becomes vacant, the commissioners of the authority shall select one of their number as chairman. The commissioners also shall select one of their number as vice chairman. Three commissioners constitute a quorum for the conduct of the business of the authority. Action may be taken by the authority upon a vote of a majority of the commissioners present unless the bylaws of the authority require a larger number.