Exercise · ZW-MULTINOMIAL-COEFFICIENT-007 · ★★☆ Intermediate
Seven distinct people are split into labeled groups A, B and C of sizes 3, 2 and 2. How many ways are there?
Choose one option.
Show answer
- B. 210
Explanation
It is \(\binom{7}{3,2,2}=\frac{7!}{3!\,2!\,2!}=210\).
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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