Asymptotic error rate expressions are derived for multi-branch equal gain combining and selection combining operating on arbitrarily correlated Rayleigh fading channels. These closed-form solutions are used to provide rapid and accurate estimation of the error rates in large signal-to-noise ratio regions. More importantly, it is shown that the asymptotic error rates over correlated branches can be obtained by scaling the asymptotic error rates over independent branches with a factor, det(M), where det(M) is the determinant of the normalized channel correlation matrix.