We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero temperature. We show that correlations between opposite momentum states, which are an important identifying characteristic of long-range order in weakly interacting Bose systems, are suppressed and that the full distribution of the number of bosons with nonzero momentum is exponential. The distribution of the quasicondensate is however quasi-Gaussian. The experimental relevance of our findings for recent cold-atom experiments is discussed.