Let a die be rolled \(n\) times. Let the probability of getting odd numbers seven times be equal to the probability of g…

Let a die be rolled \(n\) times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is \(\frac{k}{2^{15}}\), then \(k\) is equal to:

[JEE Main 2023, 10 Apr (Shift 2)]