I can do this by choosing the president first, and then the vice-president. If I choose a boy as the president, then I have 10 choices for him, and then 10 choices for the vice-president, who must be a girl. Similarly, if I choose a girl as the president, then I have 10 choices for her, and then 10 choices for the vice-president, who must be a boy. So, the total number of ways to choose a president and a vice-president of different genders is 10 times 10 plus 10 times 10, which is 200.


Our club has 20 members, 10 boys and 10 girls.  In how many ways can we choose a president and a vice-president if they must be of different gender?