The "Volunteers' Dilemma model which was introduced by Andreas Diekmann is a game theoretic model of diffusion of responsibility where only one person is needed to perform a publicly beneficial act, but many people could do it. Players do not know what the others have done. In the symmetric mixed strategy Nash equilibrium for this game, the probability that nobody takes action increases as the number of players increases. This paper shows that the same result holds even when volunteers are taken anonymously but only one person is selected to perform the action/