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There were 13 students running in a race. How many different arrangements of first, second, and third place are possible?
Answer:

There were $13$ students running in a race. How many different arrangements of first, second, and third place are possible? $\newline$ Answer:

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Experimental probability

Full solution

Q. There were

13

students running in a race. How many different arrangements of first, second, and third place are possible?

\newline

Answer:

Choose First-Place Winner: Determine the number of ways to choose the first-place winner. $\newline$ Since there are $13$ students running in the race, any one of the $13$ can come in first place. $\newline$ Calculation: There are $13$ choices for the first place.
Choose Second-Place Winner: Determine the number of ways to choose the second-place winner. $\newline$ After the first place has been chosen, there are $12$ students left who can come in second place. $\newline$ Calculation: There are $12$ choices for the second place.
Choose Third-Place Winner: Determine the number of ways to choose the third-place winner. $\newline$ After the first and second places have been chosen, there are $11$ students left who can come in third place. $\newline$ Calculation: There are $11$ choices for the third place.
Calculate Total Arrangements: Calculate the total number of different arrangements for the first three places. $\newline$ To find the total number of different arrangements, we multiply the number of choices for each position. $\newline$ Calculation: $13$ choices for first place $\times 12$ choices for second place $\times 11$ choices for third place $= 1716$ different arrangements.

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