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).

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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).

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Answer:The correct answer is 4294967296 possible ways to complete such a test.Step-by-step explanation:Step 1The 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 [tex]n_1[/tex]  ways to complete the first step, [tex]n_2[/tex] ways to complete the second step, [tex]n_3[/tex], and [tex]n_k[/tex] ways to complete the [tex]k^{th}[/tex] step, this process can be carried out in  [tex]n_1\times n_2\times n_3\times ...\times n_k[/tex] ways.Step 2We use the fundamental principle of counting with [tex]n=4[/tex] for a total of [tex]k=16[/tex] steps.  This test can be carried out in [tex]4^{16}=4294967296[/tex] ways. This comes from multiplying 4 by itself 16 times.

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