MHT CET · Maths · Sets and Relations
If \(n(A)=4, n(B)=2\). Then the number of subsets of the set \(\mathrm{A} \times \mathrm{B}\) each having at least 3 elements are
- A 275
- B 510
- C 219
- D 256
Answer & Solution
Correct Answer
(C) 219
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{n}(\mathrm{A})=4, \mathrm{n}(\mathrm{B})=2 \\ & \therefore \quad \mathrm{n}(\mathrm{A} \times \mathrm{B})=4 \times 2=8 \\ & \text { Required numbers }={ }^8 \mathrm{C}_3+{ }^8 \mathrm{C}_4+\ldots+{ }^8 \mathrm{C}_8 \\ &=2^8-\left({ }^8 \mathrm{C}_0+{ }^8 \mathrm{C}_1+{ }^8 \mathrm{C}_2\right) \\ &=256-37 \\ &=219\end{aligned}\)
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