# 004 Sample Final A, Problem 18

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Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (simplify your answer to a single number)

Foundations
If there are n teams, how many ways can first prize be awarded?
Each team could win first place. So, there are n ways that first prize can be awarded.

Solution:

Step 1:
There are 10 ways that first prize could be awarded.
Step 2:
After choosing a first place winner, there are 9 ways that second prize could be awarded.
Step 3:
After choosing both a first and second place winner, there are 8 ways that third prize could be awarded.
Step 4:
So, the total number of ways first, second, and third prizes can be awarded is ${\displaystyle 10\cdot 9\cdot 8=720}$.
${\displaystyle 720}$