I'm studying for an exam and my study guide explained combinations, permutations, and binomial distributions, but didn't cover much how to recognize where each comes into play in problems. I'm having trouble formulating the following example problem:
An operator is to operate three different switches from a group of seven. It is known that three of the seven are inoperable. If the switches are selected at random, what is the probability that two will be inoperative?
It seems like it should be a binomial process of two successes (inoperative switch) out of three trials (chosen switches) with a probability of 3/7 (three inoperative switches out of seven on the panel). However, my result, 108/343, does not match any of the given options:
3/7, 9/14, 12/35, 18/42
Assuming there's no misprint in my study guide, where am I going wrong in my formulation of the problem?