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Arrangements of letters in a word
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Learn it n different letters can be arranged in n! ways. If some letters repeat, divide by the factorial of each repeat count, because swapping identical letters makes no new word.
Example: How many arrangements of BANANA?
- 6 letters: $6! = 720$.
- A repeats 3 times and N repeats 2 times.
- $\frac{720}{3! \times 2!} = \frac{720}{12} = 60$.
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