Exercise · ZW-MULTINOMIAL-COEFFICIENT-008 · ★★☆ Intermediate
How many distinct anagrams does the word PEPPER have?
Choose one option.
Show answer
- A. 60
Explanation
They are \(\frac{6!}{3!\,2!\,1!}=60\), since P repeats three times and E twice.
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 \(k_1+\cdots+k_m=n\).
\[\binom{n}{k_1,\dots,k_m}=\frac{n!}{k_1!\,k_2!\cdots k_m!}\]
More practice problems: multinomial coefficient
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- ZW-MULTINOMIAL-COEFFICIENT-004 Compute binom62,2,2.
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- ZW-MULTINOMIAL-COEFFICIENT-006 Find the coefficient of x^2yz in (x+y+z)^4.
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- ZW-MULTINOMIAL-COEFFICIENT-009 Nine distinct books are placed on 3 identical shelves, 3 books per shelf. How many distinct distrib…
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