Question: A dice is rolled six times. Find the probability that a three is rolled exactly twice.
My thoughts: I thought i could do (1/6)(1/6)(5/6)(5/6)(5/6)(5/6), because (1/6)(1/6) accounts for the two three's, and the (5/6)(5/6)(5/6)(5/6) accounts for the other four rolls, being anything but a three. Apparently this is wrong, because i get: 625/46656, and the correct answer is: 3125/15552.
Any suggestions? help is appreciated.