[Combinatorics]
Problem: Let $T=\frac{1}{6084}$. Compute the least positive integer $n$ such that when a fair coin is flipped $n$ times, the probability of it landing heads on all $n$ flips is less than $T$.

Solution: The problem is equivalent to finding the least integer $n$ such that $\frac{1}{2^{n}}<T$, or $2^{n}>\frac{1}{T}=6084$. Because $2^{12}=4096$ and $2^{13}=8192$, the answer is $\mathbf{1 3}$.

Final answer: 13