{"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\nbecause it contains at least $1$ digit less than $1$, at least $2$ digits less than $2$, at least $3$ digits less\nthan $3$, and at least $4$ digits less than $4$. The string $23404$ does not satisfy the condition because it\ndoes not contain at least $2$ digits less than $2$.)\n\n$\\textbf{(A) }500\\qquad\\textbf{(B) }625\\qquad\\textbf{(C) }1089\\qquad\\textbf{(D) }1199\\qquad\\textbf{(E) }1296$", "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
\nbecause it contains at least 1 digit less than 1 , at least 2 digits less than 2 , at least 3 digits less
\nthan 3 , and at least 4 digits less than 4 . The string 23404 does not satisfy the condition because it
\ndoes not contain at least 2 digits less than 2 .)

\n

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

\n

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": 4, "problem_name": "2022 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p25", "prev": "/problem/22_amc10A_p23"}}