Exercise · ZW-MULTINOMIAL-COEFFICIENT-005 · ★☆☆ Basic
How many distinct anagrams does the word AAB have?
Choose one option.
Show answer
- D. 3
Explanation
It is \(\binom{3}{2,1}=\frac{3!}{2!\,1!}=3\): ABA, AAB and BAA.
Review the concept: Multinomial coefficient
Multinomial coefficient \(\binom{n}{k_1,\dots,k_m}\): the number of ways to split \(n\) distinct objects into \(m\) labeled groups of sizes \(k_1,\dots,k_m\), where \(k_1+\cdots+k_m=n\).
\[\binom{n}{k_1,\dots,k_m}=\frac{n!}{k_1!\,k_2!\cdots k_m!}\]
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