A telephone communication system is set up at a company where 125 executives are employed. The system is initialized by the president, who calls her four vice presidents. Each vice president then calls four other executives, some of whom in turn call four others, and so on. (Each executive who does make a call will actually make four calls.)
a) How many calls are made in reaching all 125 executives?
b) How many executives, aside from the president, are required to make calls?