Exercise · ZW-MULTINOMIAL-COEFFICIENT-003 · ★☆☆ Basic
Compute \(\binom{5}{2,3}\).
Choose one option.
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- B. 10
Explanation
With two groups the multinomial is a binomial: \(\binom{5}{2,3}=\binom{5}{2}=10\).
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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