there are 7 runners on the track team.runners will be selected randomly for first,second,third and final positions on 4 member relay team.
a)how many different relay teams can be formed?
b)what is the probability that a runner at random is chosen to be in the relay team? I got 7/840. Plz help
Hi! i think there can be two teams but one team will have 3 players and another can have 4 players.
So idk i guess it would be 1 team
To solve this problem, we can use the concept of permutations and combinations.
a) To find the number of different relay teams that can be formed, we need to calculate the number of ways we can select runners for each position on the team.
For the first position, we can choose any of the 7 runners. For the second position, we can choose from the remaining 6 runners. For the third position, we can choose from the remaining 5 runners. And finally, for the fourth position, we can choose from the remaining 4 runners.
So, the total number of different relay teams that can be formed is: 7 * 6 * 5 * 4 = 840
b) To find the probability that a runner chosen at random is selected to be in the relay team, we need to calculate the probability of selecting any one runner out of the total 7 runners.
The probability of selecting a specific runner is 1/7, as there is only 1 way to select that runner out of the 7 available runners.
Since we are looking for the probability of selecting any runner from the 7, we add up the probabilities for each runner.
So, the probability of selecting a runner at random to be in the relay team is: 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 + 1/7 = 7/7 = 1.
Therefore, the correct probability is 1, not 7/840.