The head of each department may select and remove all appointees in the department except as otherwise provided in this constitution, or by law. All employees in the state eleemosynary and penal institutions, and other state employees as provided by law, shall be selected on the basis of merit, ascertained as nearly as practicable by competitive examinations; provided that any honorably discharged member of the armed services of the United States who is a citizen of this state shall have preference in examination and appointment as prescribed by law.