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If \(S={2,4,8,16,...,512}\) If S is broken in 3 equal subsets A, B and C such that \(A\cap B=B\cap C=C\cap A=ϕ\) and \(A…

Q1

If \(S={2,4,8,16,...,512}\) If S is broken in 3 equal subsets A, B and C such that \(A\cap B=B\cap C=C\cap A=ϕ\) and \(A\cup B\cup C=S\), then maximum number of ways to break is:

[JEE Main 2024]

a

\({}^{9}C_{3}\)

b

\(\frac{9!}{(3!{)}^{3}}\)

c

\(\frac{9!}{(3!{)}^{4}}\)

d

\(\frac{9!}{(3!{)}^{2}}\)

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