Question 1157483
.


You should calculate the TOTAL possible number of combinations,


and then SUBTRACT from it the number of PROHIBITED combinations.


Does it work for you ?


Does it give you the right idea on how to move ahead ?



You may report me about your progress.


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On Combinations,  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>

&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>

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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Comment from student: Thanks for your reply but I can't get the idea to calculate the prohibited combination 
My new calculation : (5c3 X 6c4)-(5c4x5c3)=100 Still didn't get the correct answer...
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<U>My response</U> :


<pre>
    The number of all combinations of 4G from 6G  is  {{{C[6]^4}}}.

    Of them, the prohibited combinations are those that contain these two anti-pathic girls.

    The number of these prohibited combinations for girls is  {{{C[4]^2}}}:  

         you construct these prohibited combinations taking 2 antipathic girls, 

         and then you add to them 2 girls from remaining 6-2 = 4 "regular" girls.


    So, for girls the number of prohibited teams is {{{C[4]^2}}} = {{{(4*3)/(1*2)}}} = {{{12/2}}} = 6.

    You should combine them with all possible teams of boy, and it is what you should subtract from yours very first and most bigger number.
</pre>

That's all.


Please let me know, if you do understand my explanations, and also whether you were able to complete the solution in full.


Happy solving (!)



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<U>Comment from student</U> :  I have fully understand your explanation Thank you!!!!!

 (5c3 x 6c4)-(5c3 x 4c2) = 90
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<U>My response</U> :  You are absolutely right.


Your answer is correct !


My congratulations !


I am very glad to see your progress.


It is our common achievement: my in explanation, your in understanding.


To celebrate this breakthrough, I have a gift for you.


It is the list of additional (introductory) problems in elementary theory of probability in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Simple-and-simplest-probability-problems.lesson>Simple and simplest probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-probability-problems-using-complementary-probability.lesson>Solving probability problems using complementary probability</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A> (*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-True-False-test.lesson>A True/False test</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-multiple-choice-answers-test.lesson>A multiple choice answers test</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-probability-problems-from-the-archive.lesson>Typical probability problems from the archive</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Experimental-probability-problems.lesson>Experimental probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-operations-on-sets-help-solving-Probability-problems.lesson>Elementary operations on sets help solving Probability problems</A> 


Although these problems are on Probability theory, they have many in common with Combinatorics problems.

In particular, the lesson, marked (*) in the list, contains many problems, that are close to the solved current problem.


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>Solved problems on Probability</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.


Consider these lessons as your textbook,  &nbsp;handbook,  &nbsp;a Solutions Manual, &nbsp;tutorials and &nbsp;(free of charge)  &nbsp;home teacher.

Happy learning (!)



Come again to this forum soon to learn something new (!)