JEE 2023 — Mathematics PYQ

Since, $n(A)=5$, $n(B)=2$
$\Rightarrow n(A\times B)=n(A)\times n(B)$
$=5\times 2=10$

So, number of subsets having 3 elements=${}^{10}{C}_3$

Number of subsets having 4 elements=${}^{10}{C}_4$

Number of subsets having 5 elements=${}^{10}{C}_5$

Number of subsets having 6 elements=${}^{10}{C}_6$

∴ No. of subsets=${}^{10}{C}_3{+}^{10}{C}_4{+}^{10}{C}_5{+}^{10}{C}_6$

$=120+210+252+210=792$