Question

a shirt comes in 8 different colors, 4 different collar styles, and 3 different types of sleeves. which of the following represents the number of different combinations of colors, collars, and sleeves? a. 8 + 4 + 3 b. (8 + 4)3 c. (3 + 4)8 d. (8 + 3)4 e. 8 × 4 × 3

Explanation:

Step1: Apply the fundamental counting principle

The fundamental counting principle states that if there are \(m\) ways to do one thing, \(n\) ways to do a second thing, and \(p\) ways to do a third thing, then there are \(m\times n\times p\) ways to do all three things together.
Here, \(m = 8\) (number of color choices), \(n=4\) (number of collar - style choices), \(p = 3\) (number of sleeve - type choices).
The number of combinations is \(8\times4\times3\).

Answer:

E. \(8\times4\times3\)