Consider all strictly decreasing functions from $\{1,2,3,4\}$ to $\{1,2,3,4,5,6\}$, or in other words, all functions defined on $\{1,2,3,4\}$ such that $f(1)>f(2)>f(3)>f(4)$. Draw a decision tree so that the leaves are in lexicographical order when read from left to right. Then answer the following questions:
(a) What is the rank of $5431$?
(b) What function has rank $0$?
I have been looking all over the internet but I could not find a good resource for decision tree. I would be very appreciate it if anyone could show me how to approach this problem. Thanks