#### 698Question: A statistician is analyzing a dataset with 10 variables. How many ways can she select a subset of variables containing at least 2 and at most 5 variables, ensuring that no two selected variables are adjacent in the datasets ordering?

Mon, 04 May 2026 03:50:14 +0000

#### #### 698Question: A statistician is analyzing a dataset with 10 variables. How many ways can she select a subset of variables containing at least 2 and at most 5 variables, ensuring that no two selected variables are adjacent in the datasets ordering? When working with complex datasets, understanding how to select meaningful combinations—without missing critical constraints—is key. This precise challenge arises when a statistician aims to pick 2 to 5 variables from a sequence of 10, with the added rule that no two selected variables sit next to each other. This type of problem reflects a core concern in data modeling: balancing flexibility with structural integrity. Recent interest in efficient data selection has grown across industries relying on analytics, from market research to academic modeling. #### Understanding the Problem
The dataset’s variables are arranged linearly—each numbered from 1 to 10. The constraint that no two chosen variables can be adjacent means selections must maintain space between any two items. For example, picking variables 2 and 4 is valid, but 2 and 3 is not. This requirement is increasingly relevant as researchers seek robust, non-overlapping variable sets to avoid biased results. Chosen subsets must also range from 2 to 5 elements to preserve analytical completeness. #### Step-by-Step Calculation
To solve this, we count valid combinations across subset sizes 2, 3, 4, and 5, applying a systematic approach.