If P(S) denotes the set of all subsets of a g | vedclass

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Question

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.&nbsp

Vedclass · Accepted Answer

$336$

Vedclass · Answer

Let $S = \left\{ {1,2,3} ight\} \Rightarrow n\left( S ight) = 3$

Now, $P\left( S ight) = $ set of all subsets of $S$ total no. 

of subsets $ = {2^3} = 8$

$	herefore n\left[ {P\left( S ight)} ight] = 8$

Now, number of one-to-one functions from

$S 	o P\left( S ight)$ is ${\,^8}{P_3} = \frac{{8!}}{{5!}} = 8 	imes 7 	imes 6 = 336$.

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

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