Question 1 of 10
Multiple Choice: Please select the best answer and click "submit."
A closet contains 8 pairs of pants, 10 shirts, and 4 pairs of shoes. How many leaves on a tree diagram would represent all possible combinations of outfits?
A. 80
B. 22
C. 140
D. 320
Please make sure to post your answer with your question so you don't get in trouble for cheating :)
320
To find the answer to this question, we need to understand the concept of a tree diagram. A tree diagram is a way to represent all the possible outcomes or combinations of a sequence of events.
In this case, we are considering the combinations of outfits using pants, shirts, and shoes. We have 8 pairs of pants, 10 shirts, and 4 pairs of shoes.
To create a tree diagram, we start by drawing a tree trunk with branches representing each choice at each stage. In this case, we can start with three branches representing the choices of pants, shirts, and shoes.
At the first stage, we have 8 choices of pants, and for each of those choices, we have 10 choices of shirts. So the branches representing each choice of pants will have 10 branches coming out of them, each representing a choice of shirt.
For each combination of pants and shirt, we also have 4 choices of shoes. So each of the 80 branches representing a combination of pants and shirt will have 4 branches coming out of them, each representing a choice of shoes.
To find the total number of leaves on the tree diagram, we need to multiply the number of branches at each stage. In this case, we have 8 branches at the first stage (choices of pants), 10 branches at the second stage (choices of shirts for each choice of pants), and 4 branches at the third stage (choices of shoes for each combination of pants and shirts).
Therefore, the total number of leaves on the tree diagram, which represents all possible combinations of outfits, is 8 * 10 * 4 = 320.
So the correct answer is D. 320.