Exercise · ZW-PERMUTATIONS-WITH-REPETITION-001 · ★☆☆ Basic
How many distinct arrangements do the letters of the word AMAMA have?
Choose one option.
Show answer
- C. \(10\)
Explanation
There are 5 letters, with A repeated 3 times and M repeated 2 times: \(\dfrac{5!}{3!\,2!}=10\).
Review the concept: Permutations with repetition
The permutations with repetition of \(n\) objects, of which \(n_i\) are indistinguishable of a single type \(i\) (\(i=1,\dots,k\)), are their distinguishable arrangements in a row.
\[\dfrac{n!}{n_1!\,n_2!\cdots n_k!}\]
More practice problems: permutations with repetition
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