When are the arrangements in combinations added and multiplied?

In combinatorics, arrangements in combinations are multiplied when you are selecting items from different groups or categories, and you want to find the total number of ways to choose one item from each group. For example, if you have two groups and you can choose one item from each, you multiply the number of choices from each group. Conversely, arrangements in combinations are added when you are considering mutually exclusive options within the same category, where the total number of combinations is the sum of the combinations for each individual option.