What is the law for the distribution of two elements $\{0, 1\}$ to a set consisting of two elements(Tuples[{0, 1}, 2])
An example can be a way you two distribution $\{0, 1\}$ on a set of two elements, taking into account the order of items.(Permutations)
I know that the probability of ranking will be so, $$\{\{0, 0\}, \{0, 1\}, \{1, 0\}, \{1, 1\}\}$$ But, what is the mathematical law that formed these totals in the form of last?
What is the law of mathematics that creates the sets, $$\{\{0, 0\}, \{0, 1\}, \{1, 0\}, \{1, 1\}\}$$ depending on the distribution?
You are looking for the Cartesian product. The reason the Mathematica command is Tuples is that tuples care about order and can have multiple elements the same. In your last line $\{1,1\}$ is the same set as $\{1\}$ because sets cannot have elements the same. Also $\{0,1\}=\{1,0\}$ because sets do not care about order.