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Question

The number of one one onto functions that can be defined from A={a,b,c,d} into B={1,2,3,4} is

  1. 12    
  2. 24    
  3. 18    
  4. 26    

Hint:

Use the cardinality of two sets to find the number of one-one functions between them.

The correct answer is: 24


    STEP BY STEP SOLUTION
    Number of one-one functions = scriptbase P subscript m space end subscript space i f space n greater or equal than m end scriptbase presuperscript n
    Number of one-one functions = 0 if n less than m
    As we know the given set A & B is
    A = open curly brackets a comma b comma c comma d close curly brackets and B = open curly brackets 1 comma 2 comma 3 comma 4 close curly brackets
    Here cardinality of A =open vertical bar A close vertical bar space equals 4
    Cardinality of B =open vertical bar B close vertical bar space equals 4
    Number of one-one functions = scriptbase P subscript m space end subscript space i f space n greater or equal than m end scriptbase presuperscript n
    We can see that n=m
    So, the number of one-one functions = scriptbase P subscript 4 end scriptbase presuperscript 4
    By using the formula,
    scriptbase P subscript m space end subscript space equals end scriptbase presuperscript nfraction numerator n factorial over denominator left parenthesis n minus m right parenthesis factorial end fraction
    scriptbase P subscript 4 space equals fraction numerator 4 factorial over denominator left parenthesis 4 minus 4 right parenthesis factorial end fraction end scriptbase presuperscript 4
    The total number of one-one functions = 24

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