CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find the number of all onto functions from the set 1,2,3,....,n to itself.


Open in App
Solution

Step 1: Compute the total number of one-one functions in the set 1,2,3.

As f is onto, every element of {1,2,3} will have a unique pre-image.

ElementNumber of possible pairings
13
22
31

Total number of one-one function

=3×2×1=6

Step 2: Compute the total number of onto functions in the given set.

As f is onto, every element of {1,2,3....n} will have a unique pre-image.

ElementNumber of possible pairings
1n
2n-1
3n-2
..
..
n-12
n1

Total number of one-one function

=n×(n1)×(n2)×.×2×1=n!

Hence, the number of all onto functions from the set {1,2,3,....,n} to itself is n!.


flag
Suggest Corrections
thumbs-up
12
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Types of Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon