Question

Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a multiple-choice test consisting of 16 questions, with each question having four possible answers (a, b, c, or d).

Answer 1

Answer:

The correct answer is 4294967296 possible ways to complete such a test.

Step-by-step explanation:

Step 1

The first step is to define the fundamental principle of counting. The fundamental principle of counting states that if a process can be carried out in n steps, where there are $n_1$  ways to complete the first step, $n_2$ ways to complete the second step, $n_3$, and $n_k$ ways to complete the $k^{th}$ step, this process can be carried out in  $n_1\times n_2\times n_3\times ...\times n_k$ ways.

Step 2

We use the fundamental principle of counting with $n=4$ for a total of $k=16$ steps.  This test can be carried out in $4^{16}=4294967296$ ways. This comes from multiplying 4 by itself 16 times.