possible number of combinations of 9 elements.3 sets with 3 elements each.

Hello.new to this forum.I was trying to figure out the answer manually and ended up with 15 combinations.i couldn't find the answer by googling it maybe because i am not sure either what to type on searchbox. i remember the terms Set and Elements from college days and that's about it. i believe there is a formula also for this instance? help much appreciated.


Light to dark –borders – horizontal
light to dark –relative – horizontal
light to dark –random ov – horizontal
light to dark –borders – blotched
light to dark –borders – swirly


dark to light –borders- horizontal
dark to light –relative – horizontal
dark to light –random ov– horizontal
dark to light –borders – blotched
dark to light –borders – swirly


random or –borders – horizontal
random or–relative – horizontal
random or – randomov – horizontal
random or –borders – blotched
random or –borders – swirly

iamKJ said:

Hello.new to this forum.I was trying to figure out the answer manually and ended up with 15 combinations.i couldn't find the answer by googling it maybe because i am not sure either what to type on searchbox. i remember the terms Set and Elements from college days and that's about it. i believe there is a formula also for this instance? help much appreciated.

Order	Overlapping	Strokes
Light to dark	borders	horizontal
Dark to light	relative	blotched

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I confess that I may totally misunderstand your point. But it seems to me that:
\(\displaystyle 3\cdot 3\cdot 3\cdot=27\) is the number of combinations you offer.

iamKJ said:

Hello.new to this forum.I was trying to figure out the answer manually and ended up with 15 combinations.i couldn't find the answer by googling it maybe because i am not sure either what to type on searchbox. i remember the terms Set and Elements from college days and that's about it. i believe there is a formula also for this instance? help much appreciated.

Click to expand...

Fundamental theorem of counting: if you have "m" choices for part A and, independently, "n" choices for part B, then there are mn choices for both A and B. That can then be extended to 3 parts: if there ae "p" choice for part C, for each of those choices for A and B then there are (mn)p= mnp choices for A, B, and C.
Here A is "Order", B is "overlapping", and C is "Strokes". There are three choices for each, unless that are other condition you have not specified, there are (3)(3)(3)= 27 possible combinations.

In your first set, where the choice for "Order" is "light to dark" you have not included "relative-blotched", "relative-swirly", "random overlapping- blotched", or "random overlapping- swirly". Unless there is some reason why those cannot be matched with "light to dark" those four would give the (3)(3)= 9 possible combination with "light to dark". Similarly for the other two sets. You should have 9 combinations in each for a total of 9+ 9+ 9= 27 combinations.