A multiple-choice constraint involves selecting exactly k out of n alternatives, where k ≥ 2.Group of answer choicesTrueFalse

Analyzing the Statement

1. Understanding the Problem: The statement discusses a scenario in combinatorics where we are selecting exactly $k$ alternatives from a set of $n$ alternatives. The condition is that $k$ must be greater than or equal to 2.

2. Relevant Concepts:

   • In combinatorial mathematics, the selection of $k$ items from $n$ without regard to the order is done using the binomial coefficient, denoted as $C(n, k)$ or $\binom{n}{k}$.
   • It is possible to choose $k$ alternatives from $n$ alternatives as long as $k$ does not exceed $n$.

3. Analyzing the Statement:

   • If $k$ is at least 2, it is clear that this is a valid statement as there are numerous scenarios where selecting 2 or more options is required, such as in voting systems or team selections.

4. Verification: The requirement $k \geq 2$ simply specifies the minimum number of alternatives to be selected. Since we can choose more than one alternative (like choosing a team), the statement that we can select $k$ alternatives from $n$ when $k \geq 2$ is indeed true within the combinatorial framework.

Final Answer

True: It is possible to select exactly $k$ out of $n$ alternatives, where $k \geq 2$.