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Step 1:I'll solve this combination problem step by step using precise LaTeX formatting:
Step 2:: Understand the Combination Problem
The notation $$\binom{9}{9}$$ represents the number of ways to choose 9 items from a set of 9 items.
Step 3:: Recall the Combination Formula
\binom{n}{k} = \frac{n!}{k!(n-k)!}
The combination formula is:
Step 4:: Substitute the Values
In this case, $$n = 9$$ and $$k = 9
\binom{9}{9} = \frac{9!}{9!(9 - 9)!} = \frac{9!}{9!0!}
Step 5:: Simplify
Note that $$0! = 1$$ by definition
\binom{9}{9} = \frac{9!}{9!} = 1
Final Answer
The answer is 1, which makes sense because there is only one way to choose all 9 items from a set of 9 items.
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