In my course about machine learning I'm studying multiple linear regression and we talked about dummy variable trap. I have a data set which contains country, height, weight, gender of every person where country is encoded with letters such as us, uk, fr, ge for united states, united kingdom, france and germany respectively and genders are encoded with M F. When I convert these categorical variables into numeric ones (with one hot encoder) I get confused about the following.
When we encode M and F with two different columns if we don't drop one, we fall into dummy variable trap since a "1" on male column would obviously mean a "0" on female column therefore we only have one degree of freedom so the other is redundant, no problem here.
However with country column we can for example say a person is french if all other columns have "0" for them therefore I think that 3 columns are enough for specifying 4 countries and if we have 4 columns we would fall into dummy variable trap but all worked examples state otherwise.
Why is it so? Why 2 variables can be represented with 1 columns if two of them can't be true at the same time but 4 columns cannot be represented by 3 columns if any two columns cannot be true at the same time? Thanks in advance