Binomial distribution - is exactly what shows chance of deviation from average. If we have n trials, we have 2^n combinations of outcomes. Each outcome has x number of successes. If k outcomes have x number of successes, then chance to have outcome with exactly x successes - is k/2^n. Binomial distribution gives exactly this value. You can use any online calculator to get this value.

Again. Chance to get 1 item of 16 (actually more, but it makes things only better, not worse) - should be 1/16 in case of fair equal chances for all items. Chance to get specific duplicate 1/16*1/16, i.e. 1/256. Two duplicates in a row - 1/4096. Three - 1/65536. Etc. But there are 16 ways to get any duplicate, so chance to get any duplicate is 16 time bigger. I.e. 1/16, 1/256, etc. Let's say, we have belts. It's specific duplicate. Chance to get is - 1/256. So, you can use p=0.0078125 x=0 and then change n=1, 2, 3 etc and see, how chances to get 0, 1, 2, 3, etc. successes change. As you can see, for small number of trials - number of successes can barely be anything but 0.