@Prince Sindhiya
type the questions instead of screenshots
https://gateoverflow.in/blog/5823/screenshot
check this
related theory https://math.stackexchange.com/questions/334420/number-of-onto-functions
formula derivation is in given link
Prince Sindhiya
F(1)=4 is given and set b contain 5 element
now in set A we have total 6 element including 1
means 5 element excuding 1
given that 5 element in B
it means both set have 5 ,5 element where 1 is already related to 4
now in the remaining 5 element of A we have to relate every element of A only one element of B here we can not relate 2 element of A to the single element of B because it we do so than this will not satisfy onto property because some element will left unrelated in B
so first element of A can relate to 5 ways
and second element of A can relate to 4 ways
3 rd element 3 ways
4th element 2 ways
5th element 1 ways
so total ways is 5!
so in this process
(one thing you should note in this process 4 element of B is related to two different element of A )
Gurdeep Saini
tell me one thing
we exclude (1) from A is understandable
but why you exclude (4) from B ??
for every element y in the codomain B of f there is at least one element x in the domain A
one of the element from A {2,3,4,5,6} can map to to B (4) right ??
Prince Sindhiya clear my doubt
Magma
element 1 of A already map to 4 of B now we can ignore that elment
and do the maping of rest
what I wanted to say is that
this is possible right ??
yes @magma this is possible
but included in first case
in the first case 1 element and one other of A related to 4 of B (shown by you in figure)
but in second case only 1 element of A relate to the 4 element of B and rest elment of A relate to the remaining four element of B
@Gurdeep Saini
Good one :)
i request to the person who downvoted this answer
please tell me what is wrong so that i dont repeat this mistake in exam
who just down vote but didn't participate in the discussion, doesn't get this comment as notification
@Shaik Masthan he/she should give the reason what is wrong in this answer