Question

If P(S) denotes the set of all subsets of a given set S, then the number of one to one function from the set s={1,2,3} to the set of P(S) is

• A. 336
  
• B. 8
• C. 36
• D. 320

Answer 1

The correct option is A 336

$\begin{array}{c}Given\\ P\left(s\right)=\left\{1,2,3\right\}\\ P\left(s\right)=allsubsetof5\\ =\left\{\varphi ,\left\{1\right\},\left\{3\right\},\left\{1,2\right\},\left\{2,3\right\},\left\{3,1\right\},\left\{1,2,3\right\}\right\}\\ No.ofelementof5=0\left(5\right)=3\\ similarly\\ O\left(p\left(s\right)\right)=8\\ Totalno.ofone-onefunction\\ =\frac{n!}{\left(n-m\right)!},wheren=o\left(p\left(s\right)\right)andm=o\left(5\right)\\ =\frac{8!}{\left(8-3\right)!}=\frac{8!}{5!}\\ =336\\ No.ofone-onefunctionis336\\ Hence,optionAiscorrect,\end{array}$