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Maths-

General

Easy

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

12
24
18
26

hint 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,
$scriptbase P subscript m space end subscript space equals end scriptbase presuperscript n$ $fraction numerator n factorial over denominator left parenthesis n minus m right parenthesis factorial end fraction$
$scriptbase P subscript 4 space equals fraction numerator 4 factorial over denominator left parenthesis 4 minus 4 right parenthesis factorial end fraction end scriptbase presuperscript 4$
The total number of one-one functions = 24

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