SOLUTION: There are 12 students who wish to enroll in a particular course. There are only 4 seats left in the classroom. How many different ways can 4 students be selected to attend the clas

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Question 1160637: There are 12 students who wish to enroll in a particular course. There are only 4 seats left in the classroom. How many different ways can 4 students be selected to attend the class?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

The number of different ways is 12*11*10*9.

Solved.

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On Permutations,  see introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems (*)
    - Problems on Permutations with restrictions

    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Pay special attention to the lesson masrked (*) in the list: it is closest to your problem.

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 greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


It's astonishing how many of the problems posted on this forum are presented in a way that is unclear, or unintentionally misleading.

If the problem simply said that there were 12 students who wanted to get in the class and there was only room for 4 more, then the obvious answer for the number of ways the 4 students could be chosen would be 12C4 = 12%21%2F%28%284%21%29%288%21%29%29+=+%2812%2A11%2A10%2A9%29%2F%284%2A3%2A2%2A1%29+=+495

However, the problem stating that there are only 4 seats left in the classroom might SUGGEST that the seats are filled one at a time, making the expected answer 12P4 = 12*11*10*9 = 11880.