GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
135 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 (32.8k points)   | 135 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 (48.4k points)  
selected by
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 ago by Active (1.7k points)  


Top Users Aug 2017
  1. ABKUNDAN

    4654 Points

  2. Bikram

    4012 Points

  3. akash.dinkar12

    3136 Points

  4. rahul sharma 5

    2832 Points

  5. manu00x

    2644 Points

  6. makhdoom ghaya

    2370 Points

  7. just_bhavana

    2040 Points

  8. Tesla!

    1742 Points

  9. pawan kumarln

    1574 Points

  10. learner_geek

    1554 Points


24,864 questions
31,941 answers
74,060 comments
30,062 users