How many strings of length 5 formed from the digits 0,1,2,3,4 are there such that for each j \in\{1,2,3,4\}, at least j of the digits are less than j ? (For example, 02214 satisfies this condition because it contains at least 1 digit less than 1 , at least 2 digits less than 2 , at least 3 digits less than 3 , and at least $4$digits less than 4. The string 23404 does not satisfy the condition because it does not contain at least 2 digits less than 2.)
Answer Choices
A. 500
B. 625
C. 1089
D. 1199
E. 1296