As I understand, there are two sources of variations when growing the decisions trees of a random forest: one from the bootstrapping and another from the random selection of the variables available in your dataset that will be used to construct each tree (is this called feature section, by the way?)
Let's say I have four "independent" variables in my dataset, the Random Forest algorithm should not (or cannot?) use all of them to grow all the decision trees, but rather a random selection of, for example, two of those variables for each tree.
Is that right? Can Random Forests ever include all available variables to grow each tree or does this random variable selection always need to be present?