Question 1200705
.
<pre>

The number of different ways to select 6 students from a group of 24 students is,
BY THE DEFINITION, the number of combinations of 24 students taken 6 at a time


    {{{C[24]^6}}} = {{{24!/(6!*(24-6)!)}}} = {{{24!/(6!*18!)}}} = {{{(24*23*22*21*20*19)/(1*2*3*4*5*6)}}} = 134596.    <U>ANSWER</U>
</pre>

Solved.


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On &nbsp;Combinations, &nbsp;see introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



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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If the answer is C(24,6)*C(18,6)*C(12,6)*C(6,6), then the problem's formulation in the post is incorrect.


For this answer to be correct, the correct formulation should be as follows


<pre>
    In how many ways 24 students of the class can be distributed in 4 disjoint groups of 6 students in each group.
</pre>


It is just a bad tradition at this forum posting wrong problems.


I always say in response, that the Math education of the problems' composers at this forum
is from reading puzzles, not from learning Math.


It looks like they are not familiar with high standards of writing Math problems, at all.



Consider to hire 1 - 3 - 5 - 7 - 9 specialists, who will edit your mathematical writing on the daily basis.