Question

10 numeric 3 points how many ways can a club select a president, vice president, secretary, and treasurer from 9 members? answer

Explanation:

Step1: Identify the problem type

This is a permutation problem because the order of selection (president, vice - president, secretary, treasurer) matters. The formula for permutations of \(n\) objects taken \(r\) at a time is \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 9\) (total number of members) and \(r=4\) (number of positions to fill).

Step2: Calculate the factorial values

First, calculate \(n!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1\) and \((n - r)!=(9 - 4)!=5!=5\times4\times3\times2\times1\).

Then, \(P(9,4)=\frac{9!}{(9 - 4)!}=\frac{9!}{5!}=\frac{9\times8\times7\times6\times5!}{5!}\). The \(5!\) terms in the numerator and denominator cancel out.

Step3: Compute the result

Now, calculate \(9\times8\times7\times6=9\times8 = 72\), \(72\times7 = 504\), \(504\times6=3024\).

Answer:

3024