1989 AHSME Problems/Problem 25
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Problem
In a certain cross country meet between 2 teams of 5 runners each, a runner who finishes in the th position contributes
to his teams score. The team with the lower score wins. If there are no ties among the runners, how many different winning scores are possible?
(A) 10 (B) 13 (C) 27 (D) 120 (E) 126
Solution
The scores of all ten runners must sum to . So a winning score is anything between
and
inclusive. It is easy to check that this range is covered by considering
,
and
, so the answer is
.
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