A dorm has n suites with 3 students per suite. Find the number of ways to line the students in a row so that no suite has all 3 of its members lined
up consecutively.
Your answer may have at most one summation, and the summation must
be over a single variable. (For instance, a sum Pn
i=1 ai
is fine because
the sum is over the single variable i, but a sum over all i, j, k such that
i + j + k = n is not acceptable because it’s over the three variables i,