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If $P(S)$ denotes the set of all subsets of a given set $S$, then the number of one-to-one functions from the set $S=\{1,2,3\}$ to the $\operatorname{set} P(S)$ is
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The correct answer is:
336
336
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
$$
S \rightarrow P(S) \text { is }{ }^8 P_3=\frac{8 !}{5 !}=8 \times 7 \times 6=336 .
$$
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
$$
S \rightarrow P(S) \text { is }{ }^8 P_3=\frac{8 !}{5 !}=8 \times 7 \times 6=336 .
$$
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