JEE Mains · Maths · STD 11 - 6. permutation and combination
Let S be the set of the first 11 natural numbers. Then the number of elements in \( A=\{B\subseteq S:n(B)\ge2 \) and the product of all elements of B is even} is ___ .
- A 1979
- B 2048
- C 1984
- D 1974
Answer & Solution
Correct Answer
(A) 1979
Step-by-step Solution
Detailed explanation
A \(\{1,2,3 \ldots . .11\}\) \(\therefore n ( B ) \geq 2\) \& product of all elements in B is even Case (i) \(n(B)=2 \Rightarrow{ }^{11} C_2-{ }^6 C_2\) \(n ( B )=3 \Rightarrow{ }^{11} C _3-{ }^6 C _3\) \(n ( B )=4 \Rightarrow{ }^{11} C _4-{ }^6 C _4\)…
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