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A true-false test contains 11 questions. In how many different ways can this test be completed. (Assume we don't care about our scores.)Your answer is :

A true-false test contains 11 questions. In how many different ways can this test-example-1
User MAV
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14 votes
14 votes

Let's suppose that 1 = TRUE and 0 = FALSE, we want to find how many combinations we can do with 11 zeros and ones, in fact, it's:


\begin{gathered} \text{ 000 0000 0000} \\ \text{ 000 0000 0001} \\ \text{ 000 0000 0010} \\ \text{ 000 0000 0011} \\ ... \\ \text{ 111 1111 1111} \end{gathered}

To evaluate the number of combinations we can do:


C=2^(11)

2 because we can pick 2 different options (true or false) and 11 because it's the number of questions, then


\begin{gathered} C=2^(11) \\ \\ C=2048 \end{gathered}

We have 2048 different ways that this test can be completed.

User Mo Zaatar
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