For a 3-person relay race, a coach can choose from 4 of his top runners.how many different 3- person teams can he choose ? Use the act it out strategy.
I'm not 100 percent sure but I believe it goes like this . The coach could have runners A B C run. He could also have runners A B D run it . Yet he could have runners C A D run . He also may have Runners B D C run.
That is simply 4 "choose" 3 or C(4,3) = 4!/(3!1!) = 4
To solve this problem using the "act it out" strategy, we will simulate the process of choosing the teams using a step-by-step approach:
Step 1: List the available runners:
The coach has 4 top runners to choose from.
Step 2: Determine the first runner:
The coach needs to select the first runner for the team. He can choose from the 4 available runners. Let's call the selected runner Runner 1.
Step 3: Determine the second runner:
The coach needs to select the second runner for the team. However, since this is a relay race, we need to consider that Runner 1 has already been chosen. Therefore, there are only 3 remaining runners to choose from to pair with Runner 1. Let's call the selected runner Runner 2.
Step 4: Determine the third runner:
Similarly, the coach needs to select the third runner, considering that Runners 1 and 2 have already been chosen. There are 2 remaining runners to choose from. Let's call the selected runner Runner 3.
Step 5: Calculate the total possibilities:
Since each step involves selecting one runner out of the available options, we multiply the number of choices at each step. Therefore, the total number of different 3-person teams the coach can choose is calculated as follows: 4 choices for Runner 1 x 3 choices for Runner 2 x 2 choices for Runner 3 = 24.
Thus, the coach can choose from 24 different 3-person teams.
To find the number of different 3-person teams the coach can choose from 4 runners, you can use the "act it out" strategy. In this approach, you create a scenario and simulate the possible combinations.
Let's assign labels to the 4 runners: A, B, C, and D. Now, let's act out the process of forming the teams:
1. First, let's choose the runner for the first position in the team. We have 4 options for this position (A, B, C, or D).
2. Once we've selected the first runner, let's move on to the second position. We can choose from the remaining 3 runners since one runner is already assigned to the first position.
3. Finally, for the third position, we only have 2 runners left to choose from.
To determine the total number of teams, you need to multiply the number of choices at each step:
Number of choices for the first position = 4
Number of choices for the second position = 3
Number of choices for the third position = 2
To find the total number of teams, multiply these choices together:
Total number of teams = 4 x 3 x 2 = 24
So, the coach can choose from 24 different 3-person teams.