How Collision Probability Scales With n

Let $X_1, \dots, X_6$ be iid $\mathrm{Binomial}(n, 1/2)$, and let $p(n) = P(X_1 = X_2 = \dots = X_6).$ As $n \to \infty$, $p(n)$ decays like $c,n^{-\alpha}$ for some finite constant $c > 0$. Find $\alpha$.

Answer format: round to 1 decimal place.