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Let $\text{A}$ be a finite set having $x$ elements and let $\text{B}$ be a finite set having $y$ elements. What is the number of distinct functions mapping $\text{B}$ into $\text{A}$.

  1. $x^y$
  2. $2^{(x+y)}$
  3. $y^x$
  4. $y! / (y-x)!$
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Best answer
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Set A have x elements and B set have y elements. Each elements in B has x choices to be mapped to and being a function it must map to some element.Since each element has exactly x choices,

The total number of functions from B to A =$\underbrace{x\times x\times x\times\cdots \times x }_{y \text{ times}} \\ = x^y.$

Hence, Option(A) xis the correct choice.


For example we can consider $A = \{1\}$ and $B=\{1, 2\}$. Now, only possible function from $B \to A$ is

  1. $\{ (1,1), (2,1)\}$
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Answer : C 

I don't think this Answer need an Explanation 

Answer:

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