on 11.7 Homework
Question 7, 11.7.41
HW Score: $33.33\mathrm{\%},5$ of 15 points
Points: 0 of 1
If a club consists of 9 members, how many different arrangements of president, vice-president, and secretary are possible?

The number of possible arrangements is $◻$.

Step 1 ：We are given a club with 9 members and we are asked to find the number of different arrangements of president, vice-president, and secretary.

Step 2 ：This is a permutation problem, where order matters. We are choosing 3 people (president, vice-president, and secretary) from a group of 9.

Step 3 ：The formula for permutations is $P(n,r)=\frac{n!}{(n-r)!}$, where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

Step 4 ：Substituting the given values into the formula, we get $P(9,3)=\frac{9!}{(9-3)!}$.

Step 5 ：Calculating the factorials and simplifying, we find that the number of different arrangements is 504.

Step 6 ：Final Answer: The number of possible arrangements is $\boxed{{\displaystyle 504}}$.