GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
197 views
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
asked in Set Theory & Algebra by Veteran (39.8k points) 258 1313 1945 | 197 views

2 Answers

+5 votes
Best answer
There are n! one to one function possible with n elements to itself.. I.e. $P\binom{n}{n}$ = n!
answered by Veteran (53k points) 21 72 327
selected by
All these n! functions will also be onto and so they all are bijections ...
0 votes

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! .

answered by Boss (9.4k points) 4 8 13


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23642 Points

  2. Bikram

    17188 Points

  3. Habibkhan

    8734 Points

  4. srestha

    6404 Points

  5. Debashish Deka

    5478 Points

  6. jothee

    5098 Points

  7. Sachin Mittal 1

    4882 Points

  8. joshi_nitish

    4478 Points

  9. sushmita

    4008 Points

  10. Rishi yadav

    3960 Points


Recent Badges

Popular Question Bikram
Regular Mr.OOPs
Avid Reader Venkat Sai
Popular Question jothee
Verified Human anchal Singh
Great Question Kathleen
Verified Human Ankita_ Pawar
Avid Reader kenzou
Notable Question Sumit Chaudhary 2
Nice Comment rahul sharma 5
27,380 questions
35,231 answers
84,395 comments
33,389 users