SOLUTION: In how many ways can a group of 6 people be divided into two unequal groups if there must be at least one person in each group? I've tried combinations formula but it didnt work pl

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Question 1112258: In how many ways can a group of 6 people be divided into two unequal groups if there must be at least one person in each group? I've tried combinations formula but it didnt work plz help.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
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   =  = 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.

Solved.

-------------------
On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations

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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