Q:

Multiple Category Combination Problem

I need to figure out the total number of combinations for three categories of items which must be combined, and I'm trying to determine the appropriate way to do so. Let's say the categories are as follows:
Shirts: 3 Total, must choose 1
Ties: 18 Total, must choose 1
Additional Accessories: 20 Total, must choose 4
I must choose 1 shirt, 1 tie, and 4 accessories, which constitutes an outfit.
I understand how to develop a "normal" combinatorics problem (have 20, choose 4), but I'm not sure I understand the appropriate way to develop the total number of "outfits" from this example...What is the appropriate way to determine how many outfits can be created? Thank you in advance,

A:

The answer is
$$\binom{3}{1}\binom{18}{1}\binom{20}{4} = 261630$$
because when we make an outfit by choosing a shirt, a tie and four accessories seperately, each and every choice will be different from each other. That's why we can directly apply product rule as Useful (nevermind his current name :D) stated.

