Tests and Chances

The number of ways to select $k$ choices out of 5 is given by $\displaystyle {5 \choose k}$ . Since $1 \le k \le 5$ , the total number of ways to select at least 1 choice out of 5 is:

$\begin{aligned} N & = \sum_{\color{#3D99F6}k=1}^5 {5 \choose k} \\ & = \sum_{\color{#D61F06}k=0}^5 {5 \choose k} - \color{#D61F06}{5 \choose 0} \\ & = 2^5 - 1 \\ & = \boxed{31} \end{aligned}$

The student has a (binary) option at each of the 5 choices, whether to choose it or not.

$\text {That gives him/her } 2^5 = 32 \text { ways in total.}$

However, in one of these cases the student won't choose any of the options (despite he/she has to choose at least one (according to the question)).

Hence, our answer should be:

$32 - 1 = \boxed {31}$