MathDB
AJ basketball???

Source: 2017 AMC 12B #25

February 16, 2017
AMCAMC 122017 AMC 12B

Problem Statement

A set of nn people participate in an online video basketball tournament. Each person may be a member of any number of 55-player teams, but no two teams may have exactly the same 55 members. The site statistics show a curious fact: The average, over all subsets of size 99 of the set of nn participants, of the number of complete teams whose members are among those 99 people is equal to the reciprocal of the average, over all subsets of size 88 of the set of nn participants, of the number of complete teams whose members are among those 88 people. How many values nn, 9≤n≤20179\leq n\leq 2017, can be the number of participants?
<spanclass=′latex−bold′>(A)</span>477<spanclass=′latex−bold′>(B)</span>482<spanclass=′latex−bold′>(C)</span>487<spanclass=′latex−bold′>(D)</span>557<spanclass=′latex−bold′>(E)</span>562<span class='latex-bold'>(A) </span> 477 \qquad <span class='latex-bold'>(B) </span> 482 \qquad <span class='latex-bold'>(C) </span> 487 \qquad <span class='latex-bold'>(D) </span> 557 \qquad <span class='latex-bold'>(E) </span> 562
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