Springdale Junior High has two students, Ashley and Taylor, that qualified for the regional track meet in the 800 meter dash. The final race has only four spots available. Both Ashley and Taylor earned a spot in the final.
There are
possible finishes to the race. There are ___
finishes in which either Ashley or Taylor wins a gold medal. There are ___
finishes in which Ashley and Taylor win both the gold and silver medals.
Wrong entirely
there are a total of 24 possible outcomes to the race.
there are 12 possibilities in which either Ashley or Taylor wins a gold medal.
there are 4 possibilities in which Ashley and Taylor win both the gold and silver medals.
You're welcome
There are a total of 24 possible finishes in the race.
Now, let's break it down and find out how many finishes in which either Ashley or Taylor wins a gold medal. To do this, we need to consider the following scenarios:
1. Ashley wins gold: In this case, Taylor can finish in any of the remaining three spots in the race. So, there are 3 possible finishes where Ashley wins gold.
2. Taylor wins gold: Similarly, if Taylor wins gold, Ashley can finish in any of the remaining three spots in the race. So, there are 3 possible finishes where Taylor wins gold.
Therefore, there are a total of 3 + 3 = 6 finishes in which either Ashley or Taylor wins a gold medal.
Now let's move to the second part of the question: How many finishes in which both Ashley and Taylor win both the gold and silver medals?
Since there can only be one gold and one silver medalist, there are no finishes in which both Ashley and Taylor win both the gold and silver medals.
So, the number of finishes in which Ashley and Taylor win both the gold and silver medals is 0.
To summarize:
- Number of finishes in which either Ashley or Taylor wins a gold medal: 6
- Number of finishes in which Ashley and Taylor win both the gold and silver medals: 0
There are 4 possible finishes to the race:
1. Ashley wins gold, Taylor wins silver
2. Taylor wins gold, Ashley wins silver
3. Ashley wins gold, Taylor wins bronze
4. Taylor wins gold, Ashley wins bronze
There are 2 finishes in which either Ashley or Taylor wins a gold medal (either 1 or 2).
There is 1 finish in which Ashley and Taylor win both the gold and silver medals (finish number 1).
To answer this question, we need to determine the possibilities and outcomes of the race.
First, let's establish the total number of possible finishes in the race. Since there are four spots available, any of the four runners can finish first, followed by any of the remaining three runners in second place, then any of the remaining two runners in third place, and finally, the remaining runner would finish in fourth place. Therefore, the total number of possible finishes in the race is calculated as follows:
Number of possible finishes = 4 x 3 x 2 x 1 = 24
Now, let's determine the number of finishes in which either Ashley or Taylor wins a gold medal. Since both Ashley and Taylor earned a spot in the final, there are two possible outcomes for the gold medal winner: either Ashley wins or Taylor wins. Therefore, the number of finishes in which either Ashley or Taylor wins a gold medal is 2.
Lastly, let's determine the number of finishes in which Ashley and Taylor win both the gold and silver medals. Since there are only two spots available for the gold and silver medals, and both Ashley and Taylor earned a spot in the final, the only possible outcome is that Ashley wins the gold medal and Taylor wins the silver medal. Therefore, the number of finishes in which Ashley and Taylor win both the gold and silver medals is 1.
To summarize:
- The total number of possible finishes in the race is 24.
- The number of finishes in which either Ashley or Taylor wins a gold medal is 2.
- The number of finishes in which Ashley and Taylor win both the gold and silver medals is 1.
there are 4! possible finishes
there are 3! possible finishes if Ashley takes gold
now see what you can do