Question 10

Explanation

Identifying the Concept

This problem involves arranging $3$ people from $7$ candidates to fill specific positions (chairman, secretary, treasurer). Since the order or position matters (chairman $\neq$ secretary $\neq$ treasurer), we use the concept of Permutation.

Calculating Permutation

The formula for the permutation of $r$ objects from $n$ objects is:

Given:

• Number of candidates ($n$) = $7$
• Number of positions chosen ($r$) = $3$

Substitute into the formula:

Expand the factorials:

Thus, the number of possible staff committee arrangements is $210$ ways.