{"status": "success", "data": {"description_md": "A deck of forty cards consists of four $1$'s, four $2$'s,..., and four $10$'s. A matching pair (two cards with the same number) is removed from the deck. Given that these cards are not returned to the deck, let $\\frac mn$ be the probability that two randomly selected cards also form a pair, where $m$ and $n$ are relatively prime positive integers. Find $m+n.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

A deck of forty cards consists of four 1's, four 2's,…, and four 10's. A matching pair (two cards with the same number) is removed from the deck. Given that these cards are not returned to the deck, let \\frac mn be the probability that two randomly selected cards also form a pair, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. 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": 3, "problem_name": "2000 AIME II Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_II_p04", "prev": "/problem/00_aime_II_p02"}}