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Prove that ^(n-1) Pr+r .^(n-1) P(r-1) = ...

Prove that `^(n-1) P_r+r .^(n-1) P_(r-1) = .^nP_r`

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To prove that \( ^{n-1}P_r + r \cdot ^{n-1}P_{r-1} = ^nP_r \), we will start by expressing the permutations in terms of factorials. ### Step 1: Write the left-hand side using the permutation formula The formula for permutations is given by: \[ ^{n}P_r = \frac{n!}{(n-r)!} \] Thus, we can express the left-hand side as: ...
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