Use a tree diagram to find how many different home theater systems you can make from 6 DVD players, 8 TVs, and 3 brands of speakers.
Its 144
Oh, the possibilities! Let's dive into the world of home theater systems with a touch of humor!
We start with the DVD players as our first branch. We have 6 of them.
Next, we move on to the TVs. We have 8 TV options to choose from.
Finally, we have 3 brands of speakers to add some sound to our setups.
So, to find the total number of different home theater systems, we multiply the options at each branch: 6 DVD players * 8 TVs * 3 brands of speakers.
Calculating that, we have a grand total of 6 * 8 * 3 = 144 different home theater systems to choose from!
Now, as a loyal assistant, I have to confess that I don't mind the occasional movie marathon, but do you think you need all 144? Maybe one or two of them will be enough.
To find out how many different home theater systems can be made, we can use a tree diagram.
Step 1: Start with the DVD players. We have 6 DVD players, so we'll start by drawing 6 branches from the first level of the tree diagram, representing the different choices for the first DVD player.
Step 2: From each branch representing a DVD player, draw 8 branches for the TVs, representing the different choices for the TV.
Step 3: From each branch representing a DVD player and a TV, draw 3 branches for the brands of speakers, representing the different choices for the speakers.
Step 4: Count the branches of the final level of the tree diagram.
Here's an example of the tree diagram for this question:
DVD Player 1 DVD Player 2 ... DVD Player 6
| | |
TV 1 TV 2 ... TV 8 TV 1 TV 2 ... TV 8 TV 1 TV 2 ... TV 8
/ / /
Speaker 1 Speaker 2 Speaker 3 Speaker 1 Speaker 2 Speaker 3 Speaker 1 Speaker 2 Speaker 3
| | |
Branches Branches Branches
represents represents represents
choices for choices for choices for
DVD Player 1 DVD Player 2 DVD Player 6
Now, to find the total number of different home theater systems, we count the branches at the final level of the tree diagram. In this case, there are 6 branches at the final level.
Therefore, there are 6 different home theater systems that can be made using 6 DVD players, 8 TVs, and 3 brands of speakers.
you can make from 6 DVD players, 8 TVs, and 3 brands of speakers.
Get a LARGE sheet of paper, and draw a BIG diagram with lots of space between branches...
The tree starts with 6 branches (for the DVD's)
Coming out from the end of each branch is 8 branches (for the TV's),
then coming out from each of the TV branches are the 3 branches for the brands of speakers : )