A hundred tickets are marked $1,2,3,...100$, and they are arranged at random. 

Four tickets are picked from these and given to four persons A,B,C,D.

What is the probability that A gets the ticket with the largest value among the four of them and D gets the ticket with the smallest value?

My answer is $\displaystyle\frac{1}{12}$.
Is it correct?
Please help.