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There are 4 athletes at a track meet. How many different ways can they finish first or second?
Answer:

There are $4$ athletes at a track meet. How many different ways can they finish first or second? $\newline$ Answer:

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Find the number of outcomes: word problems

Full solution

Q. There are

4

athletes at a track meet. How many different ways can they finish first or second?

\newline

Answer:

Identify Problem Type: Identify the problem type. $\newline$ We need to find the number of different permutations of $4$ athletes finishing in the first or second place.
Calculate First Place: Calculate the number of ways to choose the first place finisher. $\newline$ There are $4$ athletes, so any one of them can finish first. Therefore, there are $4$ choices for the first place.
Calculate Second Place: Calculate the number of ways to choose the second place finisher. $\newline$ After choosing the first place finisher, there are $3$ athletes left. So, there are $3$ choices for the second place.
Use Multiplication Principle: Use the multiplication principle. $\newline$ The total number of different ways the athletes can finish first or second is the product of the number of choices for first place and the number of choices for second place. $\newline$ So, we multiply the number of choices for first place ( $4$ ) by the number of choices for second place ( $3$ ). $\newline$ $4$ choices for first place $\times$ $3$ choices for second place = $12$ different ways.

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