Permutations And Combinations Question 368
Question: The set $ S={1,2,3,…,12} $ is to be partitioned into three sets, A, B, C of equal size. Thus $ A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\phi $ . The number of ways to partition S is
Options:
A) $ \frac{12!}{{{(4!)}^{3}}} $
B) $ \frac{12!}{{{(4!)}^{4}}} $
C) $ \frac{12!}{3!{{(4!)}^{3}}} $
D) $ \frac{12!}{3!{{(4!)}^{4}}} $
Correct Answer: A $ \therefore $ The number of ways to partition $ {{=}^{12}}C_4{{\times }^{8}}C_4{{\times }^{4}}C_4 $ $ =\frac{12!}{4!8!}\times \frac{8!}{4!4!}\times \frac{4!}{4!0!}=\frac{12!}{{{(4!)}^{3}}} $
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Answer:
Solution:
BETA
