SOLUTION: A team is being formed that includes 6 different people. There are six different positions on the teams. How many ways are there to assign the six people to the six positions?

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Question 1193209: A team is being formed that includes 6 different people. There are six different positions on the
teams. How many ways are there to assign the six people to the six positions?

Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

From the context, all 6 people are equally qualified to take any of the 6 position.


So, any of the 6 people for the first position;

any of remaining 5 people for the second position;

any of remaining 4 people for the third position,


. . . and so on . . . 


giving  6*5*4*3*2*1  6! = 720 different ways.    ANSWER

Solved.

There are 6! = 720 possible permutations.

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

This problem is on  PERMUTATIONS.

On  Permutations,  see introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
in this site.

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.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

We start at 6 and count down by 1 until all six slots are full.
For more information, check out the concept dealing with factorials.
A very closely related topic would be permutations.

6 ways to fill slot A
5 ways to fill slot B
4 ways to fill slot C
3 ways to fill slot D
2 ways to fill slot E
1 way to fill slot F

There are 6*5*4*3*2*1 = 720 ways to fill the six positions where order matters.
Order matters because each position or seat is different from one another.

Answer: 720
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