Question 1112258
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<pre>
You may have these two basic configurations:


          Table

     1-st group    2-nd group
---------------------------------

1    1 persons     5 persons

2    2 persons     4 persons


And, basically, that's all.


Now we need to calculate in how many ways you can collect each configuration.


a)  Configuration #1:  1 person in one group and 5 persons in other group.


    You cam choose one person of 6 by 6 ways.

    In this way, as soon as you fill the first group, the second group is formed AUTOMATICALLY of 5 remained persons.

    So, you have 6 options/opportunities to make the configuration #1.



b)  Configuration #2:  2 persons in one group and 4 persons in other group.


    You can choose two persons of 6 by  {{{C[6]^2}}} = {{{(6*5)/2}}} = 15 ways.

    Working on this configuration, as soon as you fill the first group of 2, the second group of 4 is formed AUTOMATICALLY of 4 remained persons.

    So, you have 15 ways/options/opportunities to make the configuration #2.


c)  Since your options in Case #1  and in Case #2 are independent, you have 6*15 = 90 ways, in all, to make your selections.
</pre>

Solved.


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On Combinations, see the 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>


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.