jnu 2010 probability

[kratika]

a function is selected at random from all the functions of the set A={1,2,3......,n} into itself. the probability that the function selected is one-to-one is

a. 1/n^n
b. 2/(n-1)!
c. 1/n!
d. (n-1)!/n^n-1


is the answer option d??? plz confirm.....thanks!

[a.m]

yes Kratika . thats the answer !

[sweta]

hi how do we get that ans!

[tim]

hey am and kratika..
cn u pls give the logic for this question ??
thnk u :)

[lovekesh]

For one to one functions
i have n things on one side and n things on other side. I have to pair them that is one to one.
The no of ways it can be done is n!
total no of functions that can be made is n^n
it is so because for each number in domain, i can match it with n number in codomain.
rest u know :)

[tim]

thnk u lovekesh :)