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Sagot :
When you have a number of contestants, 18 in this instance and you need an arrangement of how to 3 different medals, that simply requires you to give all possible combinations of the first three persons assuming everyone has a chance to come either 1st, 2nd or 3rd. The formula for this type of math is shown as
[tex]P=\frac{n!}{(n-r)!}[/tex]Where P stands for the number of outcomes, n represents the number of contestants which is 18 and r stands for the number of medals to be awarded all 18 contestants. We shall now input the values into the formula. Note that the exclamation mark in the formula (!) is pronounced factorial. And it means you multiply a term by all the numbers preceding it. So 5! for example means 5 x 4 x 3 x 2 x 1, and that equals 120. For larger numbers, a calculator would come handy.
[tex]\begin{gathered} P=\frac{18!}{(18-3)!} \\ \\ P=\frac{18!}{(18-3)!} \\ \\ P=\frac{18!}{15!} \\ P=4896 \end{gathered}[/tex]Therefore the gold medal for 1st place, the silver medal for second place and the bronze medal for 3rd place can be awarded in 4896 different ways if 18 contestants are eating pies
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