SOLUTION: in aclassroom club there are 22 girls and 28 boys . the class is to elect to apresident and a treasurer. what is the number of ways for choosing these candidatess

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Question 1154704: in aclassroom club there are 22 girls and 28 boys . the class is to elect to apresident and a treasurer. what is the number of ways for choosing these candidatess
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
For each pair that is possible, call it
a and b, you can have:
[ a is pres. ] and [ b is tres. ]
[ b is pres. ] and [ a is tres. ]
so, order does matter and you will use
permutations and not combinations
whether someone is a girl or a boy
does not matter
P( n ,r ) = n! / ( n - r )!
P( n, r ) = 50! / 48!


2,450 different ways
--------------------------
feel free to get a 2nd opinion
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

In all, there are 22 + 28 = 50 students and 2 different positions.


Anyone of students can be selected for the first position, giving 50 options.


Anyone of remaining 49 students can be selected for the second position, giving 49 options.


The total number of ways is 50*49 = 2450.    ANSWER

........................

Notice, that in this problem the goal is NOT to select a pair, without looking on the order in the pair.

The goal is to select persons to certain positions, which makes the order essential.

So we use permutations --- not combinations.

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

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.


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