Group List Elements according to the Input with the order of binary combination

[quest_]

To achieve list as you present, what are the values for number?

Number (for these values ) is an integer and its value is 2 for list that I presented above. So I have 4 variable(number*2) and I will have pair binary combinations of these 4 variables (a,b),(a,bp),(ap,b),(ap,bp)

If number would be 3, this time I would have 6 variable and as a list I would have the triple binary combination of these 6 variables : (a,b,c),(a,b,cp),(a,bp,c),(a,bp,cp),(ap,b,c),(ap,b,cp),(ap,bp,c),(ap,bp,cp)