Question 1185027
.
From a group of 6 women and 8 men, a committee consisting of 4 men and 3 women is to be formed. 
how many different committees can be formed if three men refuse to serve?
~~~~~~~~~~~~~



<pre>
You can select 4 men   from a group of 8-3 = 5 men   in  {{{C[5]^4}}} = 5 different ways.

You can select 3 women from a group of 6 women in  {{{C[6]^3}}} = {{{(6*5*4)/(1*2*3)}}} = 20 different ways.


Combining these different groups of men and women, you can form the commiittee in 5*20 = 100  different ways.
</pre>

Solved.


---------------


This problem is on COMBINATIONS.

It also uses the Fundamental counting principle.


On these subjects, learn from 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/Fundamental-counting-principle-problems.lesson>Fundamental counting principle problems</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.