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General
Easy

Question

The number of into functions that can be defined from A equals left curly bracket x comma y comma z comma w comma t right curly bracket text  to  end text bold italic B equals left curly bracket bold italic alpha comma bold italic beta comma bold italic gamma right curly bracket is

 

  1. 150
  2. 0
  3. 60
  4. 243

Hint:

In this question, the number of onto functions that can be defined fromA equals left curly bracket x comma y comma z comma w comma t right curly bracket text  to  end text bold italic B equals left curly bracket bold italic alpha comma bold italic beta comma bold italic gamma right curly bracket. Formula to find the number of onto functions from set A to set B We have to find the number of onto functions from a set A with n number of elements to set B with m number of elements. Total number of functions from A to B = m to the power of n.

The correct answer is: 243


    Given, A{x, y, z, w, t} and B{alpha comma space beta comma space gamma}

    Element A can have an image in 5 ways, i.e., (x, y, z, w, t)

    Similarly, B can have an image in 3 ways.

    Thus, total number of ways =3×3×3×3×3=243


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