[Brilliant Dynamite Neon]

The most elegant way I can think to phrase this problem is:


Within a set number X of random drawings, what is the chance of producing results of Y% probability Z times within the set?


This is critical to analyze the possibilities of "generative" setups in Mafia, like C9++. You don't need to be too knowledgeable about the game to do this (although The Werewolf Game on this forum is an offshoot of it.) I'm just culling an example from it... so that it's clear what I'm talking about.

http://wiki.mafiascum.net/index.php?titl...

7 random drawings are made. I want to find out the probability that four out of those seven are Cs (a result which has a 15% chance of being drawn on any given drawing)

Therefore, in this particular instance:
X is 7
Y is 15
Z is 4

What is the general equation needed to solve this problem (and what is the answer in this particular instance, if it's not too much trouble)?