Can somebody please explain the gap and the string method used in permutations and combinations (combinatorics) to solve certain types of problems such as finding the number of arrangements when a number of objects are not together or a number of objects are always together. My teacher was talking about these and I could not understand what he was saying. I searched the internet but could not find good resources.
More information: I am in grade 11 currently and this question is relevant to the chapter Permutations and Combinations which we have in our Mathematics course. More specifically this question is relevant to questions like finding the number of arrangements when out of all objects at hand some particular objects should not be adjacent and the number of arrangements when out of all objects at hand some particular objects should always occur together. I have a basic understanding of Permutations and Combinations.