Here we need to decompose the problem into 2 subproblems :
a) Numbers which do not include zero in any of its digits..
Let we have digits w , x , y and z such that w < x < y < z..This can be done in 9C4 ways
Now according to the definition of snake like integers , the possible permutation of these digits are :
i) w y x z ii) w z x y iii) x y w z iv) x z w y v) y z w x
Hence number of valid permutations for the given selection of 4 digits = 5
Thus total number of ways under this case = 9C4 * 5
b) Numbers which include 0 :
Here we need to choose only three digits out of 9 which can be done in 9C3 ways..
Let the digits are x , y and z such that 0 < x < y < z
Now valid permutations for each selection :
i) x y 0 z ii) x z 0 y iii) y z 0 x
Hence total number of ways in this case = 9C3 * 3 ways
Thus total snake like numbers having 4 digits = 9C4 * 5 + 9C3 * 3
= 882