We study the dispersion relation for low frequency waves in the whistler mode propagating along
the ambient magnetic field, considering ions and electrons with product-bi-kappa (PBK) velocity
distributions and taking into account the presence of a population of dust particles. The results
obtained by numerical analysis of the dispersion relation show that the decrease in the j indexes in
the ion PBK distribution contributes to the increase in magnitude of the growth rates of the ion
firehose instability and the size of the region in wave number space where the instability occurs. It
is also shown that the decrease in the j indexes in the electron PBK distribution contribute to
decrease in the growth rates of instability, despite the fact that the instability occurs due to the
anisotropy in the ion distribution function. For most of the interval of j values which has been
investigated, the ability of the non-thermal ions to increase the instability overcomes the tendency
of decrease due to the non-thermal electron distribution, but for very small values of the kappa
indexes the deleterious effect of the non-thermal electrons tends to overcome the effect due to the
non-thermal ion distribution.