GATE CSE 1987 | Question: 9b

Question

How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?

Answer 1

There are $n!$ one to one function possible from a set of $n$ elements to itself.

i.e., $P\binom{n}{n} = n!$

Comments

All these n! functions will also be onto and so they all are bijections ...

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@vicky sir u are right

Answer 2

f : A---> A

∣A∣ = n

The first element of the domain has n choices for mapping,2nd element has (n-1) ,3rd element has (n-2) choices and so on.

So, total number of one-to-one functions = n ⨉(n-1)⨉(n-2)⨉(n-3).........⨉1 = n!

The correct answer is n!

Answer 3

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