what is the formula to calculate the no. of onto functions from A to B

what is the formula to calculate the no. of onto functions from A to  B


8 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

Dear prakyath

If A and B are two sets having m and n elements respectively such that   1≤n≤m  then number of onto function from A to B is

  ∑ (-1)n-r  nCr rm   r vary from 1 to n

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Rehan Vijay Jain
18 Points
10 years ago

hey can u tell me that in dis ques what shud i take the value of r

Q:- If A= {1,2,3,4}  B={4,5,6}, then find he no. of onto functions in this case.

pls tell me as fast it is possible

i need the answer of it too..........

Raawi Teza
18 Points
10 years ago

No of elements of A = 4

No of elements of B = 3

usint this formula  ∑ (-1)n-r  nCr rm   r vary from 1 to n

{[(-1)^(3-1)]*3C1*1^4} + {[(-1)^(3-2)]*3C2*2^4{ +{ [(-1)^(3-3)]*3C3*3^4}

= 1*3*1 + (-1)*3*16 + 1*1*81

= 3-48+81


18 Points
9 years ago




set a={a,b,c} and B={m,n}


the number of onto functions by your formula is 6


where as when i try manually it comes 8


according to you what should be the anwer

8 Points
9 years ago
If we calculate manually for number of onto functions from A=3 elements to B=2 elements, it comes out to be 6 as from the formula. Can anyone explain the formula.
Manas Shukla
13 Points
6 years ago
If there is set A containing a elements and set B containing b elements, formula to calculate no of onto functions is : {(b to power a)- b}
13 Points
5 years ago
n^r-nc1(n-1)^r+nc2(n-2)^r-nc3(n-3)^r.....where n=no. of elements in B;r=no. of elements in A. For a function ,f(A to B).Use this one guys ,its perfectttt.
ankit singh
askIITians Faculty 614 Points
2 years ago
Therefore, each element of X has 'n' elements to be chosen from. Therefore, total number of functions will be n×n×n.. m times = nm. For example: X = {a, b, c} and Y = {4, 5}

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