Answer :
There are 28 choices for the representative and 27 choices for the alternate, for a total of 28 * 27 = 756 possible combinations of representative and alternate.
There are 28 students in Mr. Miller's homeroom, so there are 28 choices for the student council representative. For the alternate, there are 27 remaining students to choose from (since one student has already been chosen as the representative). Therefore, there are 28 choices for the representative and 27 choices for the alternate, for a total of 28 * 27 = 756 possible combinations of representative and alternate.
It is important to note that this is a combination, not a permutation, because the order in which the representative and alternate are chosen does not matter. If the order did matter, there would be a total of 28 * 27 = 756 * 2 = 1512 possible permutations.
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