$A=\left\{1,2,3,4\right\}$ and B = {0, 1, 2, …….., 6}. A mapping $f:A\to B$ is chosen at random from set of all mappings from A to B. If ‘f’ is one-one, then the probability that the maximum element in the range of ‘f’ is 4 is 

n(s) = number of one-one functions from A to B = $\left({}^{7}P_4\right)$  
E = Event that max (f(A)) = 4
 $n\left(E\right)={(}^4{C}_1){(}^4{P}_3)$
[  one of 1, 2, 3, 4 has image 4 and other 3 elements have different images from 0, 1, 2, 3]

$P\left(\frac{E}{S}\right)=\frac{n(E\cap S)}{n\left(S\right)}=\frac{n\left(E\right)}{n\left(S\right)}=\left(\frac{4}{35}\right)$