Final answer:
There are 210 distinct ways to choose a president, vice president, and secretary from 7 eligible club members, using the permutation concept where order matters.
Step-by-step explanation:
The question deals with finding the number of distinct ways to choose a president, vice president, and secretary from a group of 7 eligible club members. This is a combinatorial problem that can be solved using permutations because order matters in the selection (the positions are distinct). To choose a president, there are 7 choices. Once a president is chosen, there are 6 remaining choices for vice president, and after that, there are 5 choices left for secretary.
The total number of ways to choose the three officers can be calculated as the product of these choices, which equals 7 × 6 × 5. This calculation gives us 210 ways to choose the officers.