# Let A and B be two sets containing 2 elements and 4 elements, respectively. The number of subsets A$$\times$$B having 3 or more elements is

## Solution :

Given, n(A) = 2 and n(B) = 4

$$\therefore$$ n(A$$\times$$B) = 8

The number of subsets of (A$$times$$B) having 3 or more elements = $$^8C_3 + {^8C_4} + ….. + {^8C_8}$$

= $$2^8 – {^8C_0} – {^8C_1} – {^8C_2}$$

= 256 – 1 – 8 – 28 = 219     [$$\because$$ $$2^n$$ = $$^nC_0 + {^nC_1} + ….. + {^nC_n}$$]

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