{"status": "success", "data": {"description_md": "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 $2$.)\n\n$\\textbf{(A) }500\\qquad\\textbf{(B) }625\\qquad\\textbf{(C) }1089\\qquad\\textbf{(D) }1199\\qquad\\textbf{(E) }1296$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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.)

\\textbf{(A) }500\\qquad\\textbf{(B) }625\\qquad\\textbf{(C) }1089\\qquad\\textbf{(D) }1199\\qquad\\textbf{(E) }1296

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2022 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12A_p25", "prev": "/problem/22_amc12A_p23"}}