AIME II 2026 (Problem 5)

An urn contains

n

marbles. Each marble is either red or blue, and there are at least 7 marbles of each color. When 7 marbles are drawn randomly from the urn without replacement, the probability that exactly 4 of them are red equals the probability that exactly 5 of them are red. Find the sum of the five least values of

n

for which this is possible.