The hook-length formula is a combinatorial formula that counts the number $f^\lambda$ of Young tableaux of a given shape $\lambda$. In this talk, we will first begin with a quick introduction to the notion of Young tableaux. Then, we will state the hook-length formula and give a probabilistic proof of the formula from a paper by C. Greene, A. Nijenhuis and H. S. Wilf in 1979. If time permits, we will derive a determinantal formula for $f^\lambda$ as a corollary of the hook-length formula.