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 set P (S) is _______.

336

Number of elements in P (S) is $2^3 = 8$. ∴ Number of one-to-one functions from S to P (S) is ${^8C}_3×3!=336$