SOLUTION: If there are 30 students in the class and we need to select a President and Treasurer for our meetings, how many possibilities are there?

Question 1136511: If there are 30 students in the class and we need to select a President and Treasurer for our meetings, how many possibilities are there?
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
The problem asks for the number of combinations of 30 students taken 2 at a time
:
30! / (2! * (30-2)!) = (30 * 29) / 2 = 435 combinations
:
Note combination means that order of selection is not important
:

Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

In this problem, the order of persons at given positions is IMPORTANT: John as the President and Alice as the Treasurer is not the same as Alice as the President and John as the Treasurer. Therefore, the answer in this problem is 30*29 = 870. There are 30 choices to select a President from a pool of 30 students, and 29 choices to select a Treasurer among remaining 29 students. This problem is NOT ABOUT COMBINATIONS - IT IS ABOUT PERMUTATIONS. It is always so, when the problem says about selections to distinguishable named positions.

Solved.

------------------------

On Combinations and Permutations, see the lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Problems on Permutations
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations

    - OVERVIEW of lessons on Permutations and Combinations
in this site.   //   I listed here the "introductory" lessons only . . .

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

/\/\/\/\/\/\/\/\

Be aware :   the answer by @rothauserc is INCORRECT !

It is why I wrote my post !

RELATED QUESTIONS
If there are 30 students in the class and we need to elect a President and Treasurer for... (answered by ikleyn)
If there are 25 students in the class and we need to select a President and Secretary for (answered by ikleyn)
If there are 25 students in the class and we need to select a President and Secretary for (answered by ikleyn,jorel1380)
If there are 25 students in the class and we need to select a President and Secretary... (answered by greenestamps)
Suppose there are 11 students running for the offices to class president, vice president, (answered by jim_thompson5910)
There are 24 students in International Student Club. How many ways are tehre to select a... (answered by ewatrrr)
there are 18 students in a class. How can 3 of them be picked for president, vice... (answered by jim_thompson5910)
There are 20 students in a class. How many different possible arrangements can there be... (answered by stanbon)
A neighborhood association elects a president, vice president, secretary and treasurer.... (answered by checkley77)