Puzzles

Brigette wrote down a list of all 3-digit numbers. For each of the numbers on her list she found the product of the digits. She then added up all of these products. Which of the following is equal to her total?

A \(45\)

B \(45^2\)

C \(45^3\)

D \(2^{45}\)

E \(3^{45}\)