Why the mixture of *on* and *kun* readings of numbers?

Question

One thing that always puzzled me was why some terms and names that are based on numbers will mix the on and kun readings. I never really understood the rules for that, but it occurs to me that there must be some.

For example, the word yakuza is derived from 8-9-3, a no-score hand in the 花札 (hanafuda) card game. This comprises:

や — 8, ya(ttsu), a kun reading
く — 9, ku, an on reading
ざ — 3, za (for san), an on reading

Similarly, the famous Admiral Yamamoto had a given name of Isoroku (meaning, curiously, "56"), which mixed kun readings (or their variants) for 5 and 10 plus the on reading for 6.

I just want to know how to make sense of this — or if it is even necessary that it make sense. Perhaps it is simply a matter of putting together sounds that the originator(s) of the term found pleasing?

Edit: I want to add that the usages sometimes seem capricious to me, as when you hear 二人（ふたり）to refer to two people but 二人前（ににんまえ）to refer to a restaurant serving for two people or the task that two people have before them, although you can hear ふたりまえ there as well.

Answer 1

This is actually an interesting topic, here's a quote from wikipedia:

In Japanese, hybrid words are common in kango – words formed from kanji characters – where some of the characters may be pronounced using Chinese pronunciations (on'yomi, from Chinese morphemes), and others in the same word are pronounced using Japanese pronunciations (kun'yomi, from Japanese morphemes). These are known as jūbako (重箱) or yutō (湯桶) words, which are themselves examples of this kind of compound (they are autological words): the first character of jūbako is read using on'yomi, the second kun'yomi, while it is the other way around with yutō. Other examples include 場所 basho "place" (kun-on), 金色 kin'iro "golden" (on-kun) and 合気道 aikidō "the martial art Aikido" (kun-on-on).

For more in-depth reading into the topic, see here.