A volunteer tutor wants to know HOW to solve this problem. It is not
necessary to give the answer if you have explained it so that a
student can get it...
A six-sided die is cast 10 times. What is the probability that exactly
3 tosses show a perfect square on top? (I guess that would be 1 and
4?)

Let P denote a perfect square and X denote something else.  Then, for
example, the following sequence is a "good" sequence with respect to
the problem:
  PXXXPXXPXX
Furthermore, the probability of this sequence occuring is
  (2/6) * (4/6) * (4/6) * ... = (2/6)^3 * (4/6)^7.
Note that this is also the probability of any other sequence of the
P-X form is the same.  Finally, the number of such sequences is easy
to count: it is simply the number of ways of choosing 3 Ps from ten
letters, so this is (10 choose 3).

The final probability is the product of these:  (10 choose 3) * (2/6)^3 * (4/6)^7.

thanks for the comment... who was that masked man?