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A3 / B5
A3 / B5
Part of
2012 Princeton University Math Competition
Problems
(1)
2012 PUMaC Combinatorics A3 / B5
Source:
10/5/2019
Jim has two fair
6
6
6
-sided dice, one whose faces are labelled from
1
1
1
to
6
6
6
, and the second whose faces are labelled from
3
3
3
to
8
8
8
. Twice, he randomly picks one of the dice (each die equally likely) and rolls it. Given the sum of the resulting two rolls is
9
9
9
, if
m
n
\frac{m}{n}
n
m
is the probability he rolled the same die twice where
m
,
n
m, n
m
,
n
are relatively prime positive integers, then what is
m
+
n
m + n
m
+
n
?
combinatorics