The Ewens sampling formula is well-known as a distribution of a random partition of the set of integers {1, 2, ... , n}. We give the condition that the number K_n of distinct components of the formula converges to the shifted Poisson distribution. Based on this convergence, we give the new approximations to the distribution of K_n, which are different from the approximations by Arratia et al. (2000, 2003). The formers are better than the latters. This is shown by comparing the bounds for the total variation distances between the distributions of the approximations and the distribution of K_n. Several examples are given to illustrate the results.