Question

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 :

Answer 1

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.