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`        what is the formula to calculate the no. of onto functions from A to  B`
7 years ago

147 Points
```										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

Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
```
7 years ago
Rehan Vijay Jain
18 Points
```										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..........
```
5 years ago
Raawi Teza
18 Points
```										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
=36
```
5 years ago
namita
18 Points
```										HI

For
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
```
4 years ago
Abishek
8 Points
```										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.
```
3 years ago
Manas Shukla
13 Points
```										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}
```
8 months ago
Torun
13 Points
```										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.
```
one month ago
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