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There are 5 athletes at a track meet. How many different ways can they finish first or second?
Answer:

There are $5$ athletes at a track meet. How many different ways can they finish first or second? $\newline$ Answer:

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Experimental probability

Full solution

Q. There are

5

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

\newline

Answer:

Understand the problem: Understand the problem. $\newline$ We need to find the number of different ways $5$ athletes can finish in the first or second place. This is a permutation problem because the order in which the athletes finish matters.
Calculate first place: Calculate the number of ways one athlete can finish first. $\newline$ There are $5$ athletes, so any one of them can finish first. This gives us $5$ possibilities for the first place.
Calculate second place: Calculate the number of ways a different athlete can finish second. $\newline$ After one athlete has finished first, there are $4$ remaining athletes who can finish second. This gives us $4$ possibilities 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 possibilities for the first place and the number of possibilities for the second place. $\newline$ So, we multiply the $5$ possibilities for the first place by the $4$ possibilities for the second place. $\newline$ $5$ (for first place) $\times$ $4$ (for second place) $= 20$
Conclude final answer: Conclude with the final answer. $\newline$ The number of different ways $5$ athletes can finish first or second is $20$ .

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