SOLUTION: How many different ways can 5 students stand in a line in the cafeteria?

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Question 1157303: How many different ways can 5 students stand in a line in the cafeteria?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

since order does not matter, use combination
5%21+=+5%2A4%2A3%2A2%2A1+=+120 different ways

Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I came to make one single correction to the post of the other tutor. 


In this problem,  the order DOES MATTER, therefore, we need use PERMUTATIONS, not combinations.


The number of all permutations of any 5 items is  5! = 5*4*3*2*1 = 120.


Solved (correctly).

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

    - 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.