sebastian is going to choose the color, patte...
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