Mathematics - Permutation & Combination Question with Solution | TestHub

$\mathrm{Y}\subseteq \mathrm{X},\mathrm{Z}\subseteq \mathrm{X}$ Let $a\in X$, then we have following chances that (1) $a\in Y,a\in Z$ (2) $a\notin Y,a\in Z$ (3) $a\in Y,a\notin Z$ (4) $a\notin Y,a\notin Z$ We require $Y\cap Z=\varphi$ Hence (2), (3), (4) are chances for '$a$' to satisfy $Y\cap Z=\varphi$. $\therefore Y\cap Z=\varphi$ has $3$ chances for $a$. Hence for five elements of $\mathrm{X}$, the number of required chances is $3\times 3\times 3\times 3\times 3=3^5$