Question

Each question on a four question multiple-choice quiz has answer choices labeled A, B, C, and D. How many different ways can a student answer these four questions?

Answer 1

When asked about the number of ways to combine, distribute, mix or divide objects, in this case answers, we use a counting method to calculate the number of possibilities.

In this case we have the possibility to respond from AAAA, AAAB, AAAC, AAAD, AABA, AABB, ..., CADB, to DDDD;  to calculate how many are we must take into account that for each possible answer of a question we have four options of the other, so, for the 4 options of question 1 we have 4 options of question 2 and for each of these, four of the question 3 and so.

Then, the answer will be 4*4*4*4 = 256 different ways for answer the questions