SOLUTION: How many ways can the positions of center midﬁelder, striker, and center back be assigned from the starting ten ﬁeld players of a soccer team?

Question 1116420: How many ways can the positions of center midﬁelder, striker, and center back be assigned from the starting ten ﬁeld players of a soccer team?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
I'm assuming (not knowing cricket) that these are unique positions that are filled by one and only one person.
Then it is 10C3=10!/7!*3!
This is 10*9*8/6=120 ways
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

In this problem the order does matter. (When the positions are named, the order of assigning DOES MATTER.) So, it is about permutations and not about combinations. The correct answer is: in 10*9*8 = 720 ways.

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
    - Arranging elements of sets containing indistinguishable elements
    - Persons sitting around a cicular table
    - Combinatoric problems for entities other than permutations and combinations
    - Miscellaneous problems on permutations, combinations and other combinatoric entities
    - OVERVIEW of lessons on Permutations and Combinations
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.

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SOLUTION: How many ways can the positions of center mid&#64257;elder, striker, and center back be assigned from the starting ten &#64257;eld players of a soccer team?

SOLUTION: How many ways can the positions of center midﬁelder, striker, and center back be assigned from the starting ten ﬁeld players of a soccer team?