Four people are chosen from a 25-member club

cyiza joseph

cyiza joseph

Answered question

2022-07-17

Four people are chosen from a 25-member club for president, vice president, secretary, and treasurer. In how many different ways can this be done?
 

Answer & Explanation

Nick Camelot

Nick Camelot

Skilled2023-06-10Added 164 answers

To find the number of different ways to choose four people from a 25-member club for the positions of president, vice president, secretary, and treasurer, we can use the concept of permutations.
Since the order in which the positions are filled matters (president, vice president, secretary, treasurer), we need to calculate the number of permutations.
The number of permutations of a set of objects is given by the formula:
P(n,r)=n!(nr)!,
where n is the total number of objects and r is the number of objects to be chosen.
In this case, we have 25 members in the club, and we need to choose 4 people for the positions.
Using the permutation formula, we have:
P(25,4)=25!(254)!.
Simplifying the expression:
P(25,4)=25!21!.
We can further simplify this by canceling out the common factors:
P(25,4)=25×24×23×22.
Evaluating the expression:
P(25,4)=30,030.
Therefore, there are 30,030 different ways to choose four people from the 25-member club for the positions of president, vice president, secretary, and treasurer.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?