# Create all possible combinations taking one item from each group

I'm not a mathematician nor is this a mathematics question per se, instead it's a real life problem I need the solution for. I have three groups of different items let's say

Group 1: T-Shirt, Solid Shirt, Patterned Shirt
Group 2: Pants, Jeans
Group 3: Blazers, Jackets, Coats, Sweaters

I need to make a list of all possible unique combinations taking one item from each group. Is there a formula of doing it?

For instance: Tshirt + Pants + Sweaters; Solid Shirt + Jeans + Blazers

• What are your thoughts? – Wojciech Karwacki Jan 5 '16 at 14:45
• Well I'm writing a blog on men's fashion and variety in fashion that can be created like Solid Shirt + Jeans + Blazer is a unique outfit. How many more like these can be created? – Vipul K Jan 5 '16 at 14:48

You can chose from the first group in $3$ way, from the second one in $2$ ways, from the third one in $4$ ways. Every choice is indipendent.
Thus you can make $3 \times 2 \times 4 = 24$ combinations.
As a general formula, if you have $n$ groups, indicating with $|Group_k|$ the number of elements of the k-th group, you can make this number of combinations:
$|Group_1| \times |Group_2| \times \cdots \times |Group_n|$.
• No! If you have a box with 15 items, and a box with 52 items, you can create $12 \times 52 = 624$ different combinations, made up of one element from the first box and one from the second one. There is no factorial in this formula. – Maffred Jan 5 '16 at 14:57