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If \ ^(n+2)C8dot\ ^(n-2)P4=57 : 16 ,\ fi...

If `\ ^(n+2)C_8dot\ ^(n-2)P_4=57 : 16 ,\ fin d\ n`

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To solve the equation \( \binom{n+2}{8} \cdot P(n-2, 4) = \frac{57}{16} \), we will break it down step by step. ### Step 1: Understand the terms The left-hand side consists of two components: - \( \binom{n+2}{8} \) is the number of combinations of \( n+2 \) items taken \( 8 \) at a time. - \( P(n-2, 4) \) is the number of permutations of \( n-2 \) items taken \( 4 \) at a time. ### Step 2: Write the formulas ...
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