QJEEM15Mabfa7: JEE Main 2015 Mathematics - Class 11 JEEM15Mabfa7 Solution: Let A and B be two sets containing four and two elements…

Given,

$$\begin{array}{rl}& n(A)=4,n(B)=2\\ \\ & \Rightarrow n(A\times B)=8\end{array}$$

Total number of subsets of set $(A \times B)=2^8$

Number of subsets of set $A \times B$ having no element (i.e. $\phi)=1$

Number of subsets of set $A \times B$ having one element $={ }^8 C_1$

Number of subsets of set $A \times B$ having two elements $={ }^8 C_2$

$\therefore$ Number of subsets having atleast three elements

$$\begin{array}{rl}& =2^8-(1+{}^8{C}_1+{}^8{C}_2)\\ \\ & =2^8-1-8-28\\ \\ & =2^8-37\\ \\ & =256-37=219\end{array}$$