Question

the local paint store offers 33 basic colors, each of which can be prepared with one of 3 different textures. how many different paint - texture pairs are possible?
there are \\(\square\\) different paint - texture pairs.
(simplify your answer.)

Explanation:

Step1: Apply the multiplication principle

The multiplication principle states that if there are \(m\) ways to do one thing and \(n\) ways to do another thing, then there are \(m\times n\) ways to do both things. Here, \(m = 33\) (number of colors) and \(n=3\) (number of textures).
$$33\times3$$

Step2: Calculate the product

Multiply 33 by 3.
$$33\times3=(30 + 3)\times3=30\times3+3\times3=90 + 9=99$$

Answer:

99