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

[quest_]

Just make variables an iterator/list whatever of integers then. Here I just set it via range, but it could be set any way.

from itertools import product
from more_itertools import grouper
import string

# create the "data"
number_pairs = 3
variables = list(range(number_pairs * 2))
print(f"variables data starts as {variables}")

number = len(variables)

groups = grouper(variables, 2)
finallist = product(*groups)
print(list(finallist))

Output:
variables data starts as [0, 1, 2, 3, 4, 5]
[(0, 2, 4), (0, 2, 5), (0, 3, 4), (0, 3, 5), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5)]

I apologise, probably it is my fault that I cannot tell what I want exactly but NO! my variables are not 0 2 4 my variables must be that

for variables in itertools.product([0, 1], repeat=(number*2))

After that I should create this groups
And after that I am writing what you recommand:

number =2
for variables in itertools.product([0, 1], repeat=(number*2)): # set of variables for a,ap,b,bp,c,cp like 000000 000001 000011....
    #a,ap,b,bp,c,cp= variables[0],variables[1],variables[2],hvariables[3] #giving value for a,ap,b,bp,c,cp
    #nlist = [(a,b),(a,bp),(ap,b),(ap,bp)] #binary combination of a,ap,b,bp,c,cp
    groups = grouper(variables, 2)
    finallist = product(*groups)
    print(list(finallist))

And I am getting this error:

Error:
raceback (most recent call last):
  File "free.py", line 151, in <module>
    groups = grouper(variables, 2)
  File "/usr/lib/python3/dist-packages/more_itertools/recipes.py", line 295, in grouper
    args = [iter(iterable)] * n
TypeError: 'int' object is not iterable

My variable is already a list !!! Why am I gettigng this error?

P.S I also wrote: variable = list(variable) but still it did not work