you are planning your outfit for a day out with friends. You have four different tops, Three different pants, and two different pairs of shoes to choose from. you are confused about which top,pants,and shoes to wear. So, you want to try different combinations to see which best suits you. How will you use the tree diagram strategy to determine how many different outfit combinations you can make? in mathematics
To determine how many different outfit combinations you can make using the tree diagram strategy, you will create a diagram that branches out for each decision you need to make. In this case, you need to make decisions about which top, pants, and shoes to wear.
Start by drawing a line as the main branch of the tree diagram. At the end of this line, label it as "Tops."
From the "Tops" branch, draw three branches, one for each top option you have. Label each branch with the corresponding top option.
From each top branch, draw three branches for the pants options. Label each branch with the corresponding pants option.
From each pants branch, draw two branches for the shoes options. Label each branch with the corresponding shoes option.
At the end of each shoe branch, indicate that it is the end of the "outfit" combination.
Count the number of end points (outfit combinations) on the tree diagram. This will give you the total number of different outfit combinations you can make.
To use the tree diagram strategy to determine the number of different outfit combinations, you will start by listing all the options for each category (tops, pants, and shoes) and then multiply the number of options in each category.
To begin, write down the four different tops as the first layer of the diagram. Let's label them as T1, T2, T3, and T4.
T1
/ \
/ \
/ \
T2 T3
\
T4
Next, for each top, write down the three different pants as the second layer of the diagram. Let's label them as P1, P2, and P3.
T1
/ \
/ \
/ \
T2 T3
/ | \ \
/ | \ \
P1 P2 P3 P1 P2 P3
Finally, for each combination of top and pants, write down the two different pairs of shoes as the third layer of the diagram. Let's label them as S1 and S2.
T1
/ \
/ \
/ \
T2 T3
/ | \ \
/ | \ \
P1 P2 P3 P1 P2 P3
/ \ / \ | \ | \
S1 S2 S1 S2 S1 S2 S1 S2
To determine the total number of different outfit combinations, count the number of endpoints in the diagram. In this case, we have 4 tops, 3 pants, and 2 shoes. So the total number of different outfit combinations is 4 x 3 x 2 = 24.
Therefore, you have 24 different outfit combinations to choose from using the tree diagram strategy.
To determine the number of different outfit combinations you can make using the tree diagram strategy, you can follow these steps:
Step 1: Start the tree diagram with the tops as the first level choice. Draw four branches representing the four different tops you have.
Step 2: For each top, draw three branches representing the three different pants. This will create a total of 4 x 3 = 12 branches at the second level.
Step 3: From each combination of top and pants, draw two branches representing the two different pairs of shoes. This will create a total of 12 x 2 = 24 branches at the third and final level.
Step 4: Count the number of branches at the final level, which represents the total number of different outfit combinations you can make. In this case, there are 24 branches, so you can make a total of 24 different outfit combinations.
Using the tree diagram strategy, you can visually organize and determine all the possible combinations by working through the branches systematically.