Problem 2.21 Each permutation of the integers {1, 2, 3, 4, 5} determines a five digit number. If the numbers corresponding to all possible permutations are listed in increasing order of magnitude, i.e., {12345, 12354,... 54321}, show that the 73rd number on the list is 41235. Hint: It is too tedious and unnecessary to list all the numbers in the list. A simple counting argument suffices.