2000 AIME II Problems/Problem 3
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Problem
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 
be the probability that two randomly selected cards also form a pair, where 
and 
are relatively prime positive integers. Find 
Solution
WLOG, assume that the pair removed is a pair of 1s. Therefore, the probability that a pair of 1's is drawn is 
.
The probability that it is a pair of 2, 3, ..., or 10 is 
. 
, and thus the answer is 
.
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