How to generate a list from permutations of other lists in Mathematica

I am stuckwith a fairly simple problem: I need to construct a list with all permutations of values from two different lists in Mathematica. Let say, a={1,2} and b={4,5} I would need the result

c={{1,开发者_如何学编程4},{1,5},{2,4},{2,5}}

Could anybody please give me an idea how to achieve this? Thanks a lot,

Philipp

Here is one way

In[2]:= Tuples[{{1, 2}, {4, 5}}]

Out[2]= {{1, 4}, {1, 5}, {2, 4}, {2, 5}}

The built-in Tuples function does precisely what you want:

In[1]:= a = {1, 2}; b = {4, 5};

In[2]:= c = Tuples[{a, b}]
Out[2]= {{1, 4}, {1, 5}, {2, 4}, {2, 5}}

You can also accomplish this using Flatten and the more general Outer:

In[3]:= Flatten[Outer[List, a, b], 1]
Out[3]= {{1, 4}, {1, 5}, {2, 4}, {2, 5}}

I mention this last fact because a lot of the time when I find myself using Tuples, I'm doing so as an intermediate step before immediately Applying a function to each of the generated sublists, and using Outer can save me a step.