Geometry

Question Analysis
This question involves a two - step process of first selecting a subset of people and then arranging them.
The main focus is on using the permutation formula to solve a complex real - world problem related to committee formation.

Key Concept Explanation
The permutation formula is used to find the number of ways to select and arrange objects out of objects.
Here, we are essentially finding the number of permutations of 4 people out of 7, as the order of people in the different positions (president, vice - president, etc.) matters.

Step - by - Step Solution
Here, (the total number of people in the group) and (the number of people to be selected and arranged in positions).
Using the formula , we substitute the values: