A French club with 10 members randomly selects its president and vicepresident. The frist name chosen is the president and the second name chosen is the vicepresident. How many different ways can a president and vicepresident be chosen. Solution You can use the multiplication principle here: There are 10 people who can be considered for president and then only 9 people remaining who could be considered for vice-president. So, there are a total of 10*9 = 90 ways that the selections could be done..