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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

Options

  1. A24
  2. B8
  3. C336
  4. D320

Correct answer

C. 336

Step-by-step solution

Let S= 1,2,3 n(S)=3 Now, P(S)= set of all subsets of S total no. of subsets =2^3=8 n[P(S)]=8 Now, number of one-to-one functions from S P(S) is ^8 P₃= 8 ! 5 ! =8 7 6=336 .

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