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Sagot :
You know that:
- There are 3 places that are to be awarded: First place, second place, and third place.
- The number of contestants in the dance contest is 12.
Then, you need to use Permutation in order to solve this exercise. Remember that, by definition:
[tex]P(n,r)=\frac{n!^{}}{(n-r)!}[/tex]Where "n" is the total number of things to choose from and "r" is the number of things chosen.
In this case, you can identify that:
[tex]\begin{gathered} n=12 \\ r=3 \end{gathered}[/tex]Then, substituting and evaluating, you get:
[tex]P(12,3)=\frac{12!^{}}{(12-3)!}=\frac{12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=\frac{479001600}{362880}=1320[/tex]Therefore, the answer is:
[tex]1320\text{ }ways[/tex]
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