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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

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    $\begingroup$ What are your thoughts? $\endgroup$ – Wojciech Karwacki Jan 5 '16 at 14:45
  • $\begingroup$ 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? $\endgroup$ – Vipul K Jan 5 '16 at 14:48
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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:

$|Group_1| \times |Group_2| \times \cdots \times |Group_n|$.

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  • $\begingroup$ So do I use something like factorials for this? $\endgroup$ – Vipul K Jan 5 '16 at 14:53
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    $\begingroup$ 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. $\endgroup$ – Maffred Jan 5 '16 at 14:57
  • $\begingroup$ Aright, I get it. Thanks mate $\endgroup$ – Vipul K Jan 5 '16 at 15:40

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