If $n(A)=4, n(B)=2$. Then the number of subsets of the set $\mathrm{A} \times \mathrm{B}$ each having at…

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
  1. 275
  2. 510
  3. 219
  4. 256

Solution

$\begin{aligned} & \mathrm{n}(\mathrm{A})=4, \mathrm{n}(\mathrm{B})=2 \\ & \therefore \quad \mathrm{n}(\mathrm{A} \times \mathrm{B})=4 \times 2=8 \\ & \text { Required numbers }={ }^8 \mathrm{C}_3+{ }^8 \mathrm{C}_4+\ldots+{ }^8 \mathrm{C}_8 \\ &=2^8-\left({ }^8 \mathrm{C}_0+{ }^8 \mathrm{C}_1+{ }^8 \mathrm{C}_2\right) \\ &=256-37 \\ &=219\end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 1)

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