I am taking Math A 30. The chapter we are doing is on Counting. This is my question.

How many boy-girl dancing couples could be formed if 85 boys and 102 girls attend a school dance?

Thank you for your time
Danielle

The problem you have is a special case of the Multiplication Principle: if you can perform a certain task in p ways and another task in q ways then the number of ways to perform these tasks one after the other is p x q.

In your problem, to create all possible boy-girl pairs, you need to first select a boy and then select a girl (or vice versa). There are 85 choices for the boy and 102 choices for the girl so the number of distinct pairs is 85 x 102 = 8670.