Mathematics - Functions Question with Solution | TestHub

Let $S=\{1,2,3\}\Rightarrow n(S)=3$ Now, $P(S)=$ set of all subsets of $S$ total no. of subsets $=2^3=8$ $$\therefore n[P(S)]=8$$ Now, number of one-to-one functions from $$S\to P(S)\text{ is }{}^8{P}_3=\frac{8!}{5!}=8\times 7\times 6=336.$$