[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
in how many ways can a first second and a third prize awarded to 10 competing teams if there are no ties
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[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
Using the Permutation Formula
- [tex]\sf{P(n,r)=\frac{n!}{(n-r)!}}[/tex]
- Given that: n = 10 and r = 3
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Solving:
[tex] \qquad \boxed{\begin{array}{}\sf{P(n,r)=\frac{n!}{(n-r)!}} \\ \\\sf{P(10,3)=\frac{10!}{(10-3)!}}\\ \\\sf{P(10,3)=\frac{10!}{7!}} \\ \\ \sf{P(10,3)=\frac{10 \times 9 \times 8 \times 7!}{7!}} \\ \\ \sf{P(10,3)=\frac{10 \times 9 \times 8 \times \cancel{ 7!}}{ \cancel{7!}}} \\ \\ \sf{P(10,3)=10 \times 9 \times 8 } \\ \\ \boxed{ \sf{P(10,3)=720}}\end{array}}[/tex]
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[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
