If P(S) denotes set of all subsets of a given set S, then number of one-to-one functions from set S

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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 set $P(S)$ is

$24$

$8$

$336$

$320$

(AIEEE-2012)

Let $S = \left\{ {1,2,3} \right\} \Rightarrow n\left( S \right) = 3$

Now, $P\left( S \right) = $ set of all subsets of $S$ total no.

of subsets $ = {2^3} = 8$

$\therefore n\left[ {P\left( S \right)} \right] = 8$

Now, number of one-to-one functions from

$S \to P\left( S \right)$ is ${\,^8}{P_3} = \frac{{8!}}{{5!}} = 8 \times 7 \times 6 = 336$.

Standard 12

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