I heard that there are roughly 400 sounds in Mandarin plus four tones. Are all combinations of those used in Chinese vocabulary, making it 1600 possibilities per single-sound word? If not, how many such combinations are actually used in any piece of a word?
I wrote a program to search through an unofficial online version of 现代汉语词典. The results show 1345 possible combinations.
Here is a list of the 1345 sounds, each with one example Chinese character (not most representative or most frequently used).
Note that I also included the neutral tone (for example ba0:吧) and a few strange ones (e.g. hm:噷, hng:哼, m1:姆, m2:呣).
Using the above list, you can easily find some "missing" combinations, e.g. an2, ang3, ban2, bang2, bei2, ben2, bian2, biao2, bin2, bin3, bing2, ca2, ca4, cang3, cang4, ce1, ce2, ce3, ...
I use this one. But it show all combinations, including ones that aren't words. http://www.quickmandarin.com/chinesepinyintable/
ETA: It has tones, if you want to hear how they sound.