To find the number of different sweatshirt designs possible for Sebastian, we use the fundamental counting principle, multiplying the number of options per category: 10 colors, 4 patterns, 12 fonts, and 9 images, resulting in 4,320 possible designs.
Step-by-step explanation:
Sebastian has a variety of options to customize a sweatshirt for his dance team, with 10 colors, 4 patterns, 12 fonts, and 9 images to choose from. To calculate the total number of possible sweatshirt designs, we need to apply the fundamental counting principle. This principle states that if there are 'n' ways to do one thing, and 'm' ways to do another thing after that, then there are n*m ways to do both.
In Sebastian's case, he has to choose one option from each of the categories, so we multiply the number of options in each category together:
10 options for colors
4 options for patterns
12 options for fonts
9 options for images
So the total number of different sweatshirt designs possible is:
10 (colors) × 4 (patterns) × 12 (fonts) × 9 (images) = 4,320 possible designs.
The probable question can be: Sebastian is going to choose the color, pattern, font, and image for the design of a sweatshirt for his dance team. There are 101010 colors, 444 patterns, 121212 fonts, and 999 images for him to choose from. (The printing company charges a fee to add extra design elements, so he will choose only one of each.) How many different sweatshirt designs are possible?