Subjects combinatorics

Using Repetition

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Using Repetition


1. The problem states that you can use the same number twice. This typically applies to problems involving combinations, permutations, or equations where repetition is allowed. 2. For example, if you are asked to find the number of ways to select numbers from a set with repetition allowed, the formula for combinations with repetition is: $$\binom{n+r-1}{r}$$ where $n$ is the number of types of items, and $r$ is the number of items chosen. 3. If the problem involves forming numbers or sequences where repetition is allowed, the total number of sequences of length $r$ from $n$ options is: $$n^r$$ 4. Using the same number twice means repetition is allowed, so you apply these formulas accordingly. 5. If you provide a specific problem, I can show detailed steps using these principles.