If it had been detected gravitational waves from merging of black holes (BH), and neutron stars (NS), why there are no detection of black holes merging with neutron stars?
Why a BH-NS merging should be a rarer event than BH-BH and NS-NS?
I don't think we have a clear answer yet. LIGO hoped to detect black hole (BH) mergers and expected to detect neutron star (NS) mergers, yet the BH mergers are observed more frequently, partly because they are louder and thus LIGO can see them from further away and partly because the 20-40 solar mass BHs LIGO observed are more common than we expected.
BHs this size can be formed by the supernova implosion of a massive star, but BHs formed this way should be quite rare They can also be formed by the merger of two smaller BHs -- which is exactly what LIGO was observing! It seems likely that these larger (but still stellar mass) BHs were produced by previous mergers.
So in the end, the frequency of LIGO detections depends on two things: The real distribution of objects in binaries: NS-NS, NS-BH, and BH-BH and the loudness/brightness of the gravitational waves emitted by the merger.
In general, black holes form from more massive stars than neutron stars, and that means rarer stars. (The moreso since the more massive a star is, the quicker it sheds mass through stellar winds.)
So NS-NS systems come from lesser-massive stellar pairs. NS-BH systems form the same way, but with one of the original stars being more massive than would lead to a NS. On the other hand, the BH-BH systems we're detecting probably come from BHs that themselves were the result of mergers in very dense stellar environments.
Consequently, we wouldn't expect that NS-BH mergers would be especially correlated with BH-BH mergers, since they precursor systems are formed through different mechanisms. But we would expect NS-BH mergers to be rarer than NS-NS mergers since the precursor systems are rarer.
There's a bit of handwaving in that! I'll try to find some papers on the subject -- there must be a bunch.