Question 1070003
So the idea is that we want to find the total number of ways that we can pick 7 diamonds (real or fake) from the 12 diamonds.  

So as you said, 12 choose 7 = 792

Now we need the total number of ways that we can satisfy that of the 7 we picked, exactly three are real, but this also means that four are fake.

So to choose 3 real from 5 is  5 choose 3 = 10

And to choose 4 fake from 7 is 7 choose 4 = 35

{{{(35*10)/792}}} = {{{350/792}}} = {{{highlight(175/396)}}}