In how many ways can a club consisting of 25 members chose a president, a secretary a treasurer, and a auditor?
This is also my homework. what is your answer here?^_^
To determine the number of ways a club can choose a president, secretary, treasurer, and auditor from a group of 25 members, we can use the concept of permutations.
Permutations represent the number of ways to arrange a set of objects in a specific order. In this case, the order in which the members are chosen for the club positions matters (i.e., the president, secretary, treasurer, and auditor are distinguishable roles).
To calculate the number of ways, we need to consider the number of choices available for each position and multiply them together.
Let's break it down step by step:
1. For the president position, there are 25 members to choose from initially.
2. After selecting the president, we have 24 members remaining to choose from for the secretary position.
3. Once the president and secretary are chosen, there are 23 members left for the treasurer position.
4. Finally, after selecting the president, secretary, and treasurer, there are 22 members remaining for the auditor position.
To calculate the total number of ways, we multiply the number of choices at each step:
Total number of ways = 25 choices for president × 24 choices for secretary × 23 choices for treasurer × 22 choices for auditor.
Therefore, the number of ways the club can choose a president, secretary, treasurer, and auditor is:
25 × 24 × 23 × 22 = 303,600 ways.
Hence, there are 303,600 ways for the club to select its members for the given positions.