sebastian is going to choose the color, pattern, font, and image for the design of a sweatshirt for his…

sebastian is going to choose the color, pattern, font, and image for the design of a sweatshirt for his dance team. there are 10 colors, 4 patterns, 12 fonts, and 9 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?

sebastian is going to choose the color, pattern, font, and image for the design of a sweatshirt for his dance team. there are 10 colors, 4 patterns, 12 fonts, and 9 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?

Answer

Explanation:

Step1: Apply counting principle

Use the multiplication - principle of counting. If there are (m_1) ways to do one thing, (m_2) ways to do a second thing, (m_3) ways to do a third thing, and (m_4) ways to do a fourth thing, then the total number of ways to do all four things together is (m_1\times m_2\times m_3\times m_4). Here, (m_1 = 10) (number of colors), (m_2=4) (number of patterns), (m_3 = 12) (number of fonts), and (m_4=9) (number of images).

Step2: Calculate the product

[10\times4\times12\times9=40\times12\times9 = 480\times9=4320]

Answer:

4320