Question

Eight people audition for a choir. the choir director must choose one soprano, one alto, and one tentor. In how many ways can this director fill these positions?

Answer 1

If we start off by choosing someone for soprano then how many choices do we have?

And then if we choose one person for alto from the remaining? And then tentor?


Here's a similar question:
We have 10 people trying to make it on a football team and there's only 3 open spots on the team. We can fill these positions in 10*9*8 different ways.
The first spot has 10 candidates. Once we fill that up, we have 9 candidates for the second spot. And then we have 8 candidates left for the third spot. So we have 10*9*8 = 720 different ways to fill up the three spots.

Hopefully that should help you be able to solve your question.