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Prove that combinatorial argument that ^...

Prove that combinatorial argument that `^n+1C_r=^n C_r+^n C_(r-1)dot`

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To prove the combinatorial identity \( \binom{n+1}{r} = \binom{n}{r} + \binom{n}{r-1} \), we can use a combinatorial argument based on selecting toys. ### Step-by-Step Solution: 1. **Understanding the Problem**: We want to select \( r \) toys from a total of \( n + 1 \) toys. The left-hand side of the equation, \( \binom{n+1}{r} \), represents the number of ways to choose \( r \) toys from \( n + 1 \) toys. **Hint**: Think about how you can categorize the selection of toys based on whether a particular toy is included in the selection. ...
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