The ternary nucleation of an ideal mixture of three alcohols and a non-ideal mixture of water, ammonia and hydrochloric acid, which is relevant in atmosphere, have been investigated theoretically. In the ideal mixture of three alcohols, the nucleation rates obtained using simplified kinetic approach are compared with the nucleation rates given by a detailed kinetic model. The simplified model is seen to underestimate nucleation rates by 2-3 orders of magnitude. This is mainly due to the crude estimate for the Zeldovich factor in the simplified model. We have proposed a modification to the simplified model. The improved model gives order-of-magnitude estimates for the nucleation rates. The ternary nucleation of water-ammonia-hydrochloric acid is studied with the improved model. The results have been compared with binary nucleation of water and ammonium chloride. The results show that water-ammonia-hydrochloric acid mixture is effectively a two-component system.