Exploring Combinations: Light Bulb Color Arrangements
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Chapter 1: The Colorful Challenge
Have you ever wondered how many different ways you can arrange light bulbs in various colors? This intriguing counting puzzle invites you to explore all possible combinations, including scenarios with each color appearing more than once. Your task is to consider arrangements involving all four colors, as well as those featuring three colors with one color duplicated.
Pause for a moment, grab a piece of paper, and see if you can work out the answer. When you're ready, continue reading for the solution!
Here’s a helpful hint: Let’s label each position with numbers.
Now, picture placing the bulbs one at a time. Remember, each bulb can be any of the four colors available.
For the first position, you have four options: red, blue, green, or yellow. That gives you 4 possibilities.
Suppose you choose red for the first position. For the second position, you must select a bulb that is not red, leaving you with three choices.
If you decide on a blue bulb for the second position, you can then opt for either green or yellow for the third. This provides you with 2 choices.
Now, here comes the crucial part: if you place a yellow bulb in the third position, you can again choose between a green or red bulb for the fourth position, giving you another 2 options.
To summarize our exploration, the total number of combinations is calculated as 4 × 3 × 2 × 2 = 48. And that’s your answer!
Bonus Puzzle: What if we add a fifth color into the mix?
How intriguing! What strategy did you use this time? Feel free to share your thoughts in the comments; I’m excited to hear your insights!
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Chapter 2: Visual Learning through Videos
In the first video, "Battery, bulb, and wires - every way to light the bulb," explore various methods of lighting a bulb using different arrangements of batteries and wires.
The second video, "Here's how to get this light bulb to glow with a battery," demonstrates a straightforward approach to illuminating a light bulb using a battery.