Question 1154056
There are {{{12*11*10*9*8=95040}}} that 5 diamonds can be picked. Instead of finding the probability that at least 2 diamonds are real, we can instead count the probability that 0 or 1 diamond is real and subtract from 1 to get the answer. The number of ways that all the diamonds picked are fake is {{{7*6*5*4*3=2520}}}. There are {{{7*6*5*4*5*5=21000}}} ways to pick one real diamond. So the number of ways that at least 2 diamonds are real is {{{95040-(2520+21000)=71520}}}. So there is a {{{71520/95040=149/198}}} or approximately 75.25% chance that at least 2 diamonds are real.