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Permutations and combinations — Permutations 56 problems

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📘 Notes

Permutations

A permutation is a way of selecting and arranging objects where order matters.

1. Key Idea

Key word: arranged.

A permutation counts arrangements where different orders produce different results.

2. Permutation Formula

Number of permutations of \(r\) objects from \(n\) distinct objects:

\[ ^nP_r=\frac{n!}{(n-r)!} \]

If all objects are arranged:

\[ ^nP_n=n! \]

3. Example

How many ways can 3 students be arranged from 5 students?

\[ ^5P_3=\frac{5!}{(5-3)!} \] \[ =\frac{120}{2}=60 \]
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