I have 3 features age, income and rating.
In case of age I have 3 buckets.
for income I have 4 buckets.
and for rating I have 2 buckets.
If one could filter data where a person could select 1 or more than 1 bucket from each feature what would be the total number of combinations that can be selected?
E.g
Age = [less than 18, 18 < age <= 30, greater than 30]
Rating = [Low, High]
Combination_1 = [less than 18, Low]
Combination_2 = [18 < age <= 30, Low]
Combination_3 = [greater than 30, Low]
Combination_4 = [less than 18, High]
Combination_5 = [18 < age <= 30, High]
Combination_6 = [greater than 30, High]
Combination_7 = [less than 18, None]
Combination_8 = [18 < age <= 30, None]
Combination_9 = [greater than 30, None]
Combination_10 = [None, Low]
Combination_11 = [None, High]
Combination_12 = [None,None]
In this example there will be 12 combinations. What would be a generalized formula to achieve this?
Here None represents nothing is filtered from the feature.
Edit:
None here is not a feature but just a representation to tell it can be possible that nothing is selected.
Combination_1 = [less than 18, Low]
Combination_2 = [18 < age <= 30, Low]
Combination_3 = [greater than 30, Low]
Combination_4 = [less than 18, High]
Combination_5 = [18 < age <= 30, High]
Combination_6 = [greater than 30, High]
Combination_7 = [less than 18, None]
Combination_8 = [18 < age <= 30, None]
Combination_9 = [greater than 30, None]
Combination_10 = [None, Low]
Combination_11 = [None, High]
Combination_12 = [None,None]
As one could select more than 1 bucket from each feature following combinations are also possible.
Combination_13 = [[less than 18,18 < age <= 30], Low]
Combination_14 = [[less than 18,18 < age <= 30], high]
Combination_15 = [[less than 18,18 < age <= 30], None]
Combination_16 = [[less than 18,18 < age <= 30, greater than 30], Low]
Combination_17 = [[less than 18,18 < age <= 30, greater than 30], high]
Combination_18 = [[less than 18,18 < age <= 30, greater than 30], None]
Combination_19 = [less than 18, [High,Low]]
Combination_20 = [18 < age <= 30, [High,Low]]
Combination_21 = [greater than 30, [High,Low]]
Combination_22 = [[less than 18,18 < age <= 30], [High,Low]]
Combination_23 = [[less than 18,18 < age <= 30], [High,Low]]
Combination_24 = [[less than 18,18 < age <= 30], [High,Low]]
Combination_25 = [[less than 18,18 < age <= 30, greater than 30], [High,Low]]
Combination_26 = [[less than 18,18 < age <= 30, greater than 30], [High,Low]]
Combination_27 = [[less than 18,18 < age <= 30, greater than 30], [High,Low]]
Best Answer
Based on all clarifications in comments, here is how you can look at the number of combinations -
Each dropdown value in the feature can be independently selected - there are $2$ options - either it is selected or not selected = 2 ways.
So for Age feature $= 2^3$ combinations, as there are $3$ dropdown values. If none the values are selected, that is included in $2^3$ combinations.
For Income feature $= 2^4$ combinations.
For Rating feature $ = 2^2$ combinations.
So total number of combinations $= 2^3 \times 2^4 \times 2^2 = 2^9 = 512$ combinations.
Please note this includes a case if none of the values from any of the features are selected (i.e. no feature is selected).