A speech class teacher is going to rank nine different speeches.  In how many different ways could she do this?   is 9P9 correct?

At the World Goldendoodle Championship, 16 doodles compete to see who is the fluffiest.  The top five contests receive prizes and cash: 1st = $300,000 2nd = $100,000 3rd = $50,000 4th = $25,000 5th = $10,000 Obviously, being first is better than being fifth.  How many ways can the 16 doodles make the top five?

can you answer 25

The party store sell balloons in 9 different colors. In how many ways can you make a selection of 15 balloons?

Ten students are going to line up at the door. In how many different ways can they line up?

How many ways can you seat 8 people around a round table? Assume that the first person can choose any seat, and it doesn't matter where that person chooses. All that matters is where the others then choose to sit. Number different ways