Let A and B Two sets containing 2 elements and 4 elements respectively. The number of subsets of A x B having 3 or more elements is

A
256
B
220
C
219
D
211

Solution:

Given,

$n (A) = 2, n (B) = 4 ∴ n (A \times B) = 8$

The number of subsets of A x B having 3 or more elements

$\begin{array}{l} =^{8} C_{3} +^{8} C_{4} + \dots +^{8} C_{8} \\ = (^{8} C_{0} +^{8} C_{1} +^{8} C_{2} +^{8} C_{3} + \dots +^{8} C_{8}) - (^{8} C_{0} +^{8} C_{1} +^{8} C_{2}) \\ ∴ 2^{n} =^{n} C_{0} +^{n} C_{1} + \dots +^{n} C_{n} \\ = 2^{8} -^{8} C_{0} -^{8} C_{1} -^{8} C_{2} +^{8} C_{1} +^{8} C_{2}) \\ = 256 - 1 - 8 - 28 = 219 \end{array}$

Solution:

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