### Instruction: 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?### Response: I need to count the number of pairs of people of different genders that I can form from the club members.
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.