Question 1195072
.
There are 13 female board members and 17 male board members.

(a) How many ways are there to make a committee of 18 board members?

(b) How many ways are there to make a committee of 18 board members if exactly 7 must be female?
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Part (a)


<pre>
There are 13 + 17 = 30 board members, in all.


There are  {{{C[30]^18}}}  different ways to select a committee of 18 board members.


Here  {{{C[30]^18}}}  is the number of combinations of 30 persons taken 18 at a time.


The formula to calculate it is this


    {{{C[30]^18}}} = {{{30!/(18!*(30-18)!)}}} = {{{30!/(18!*12!)}}} = {{{(30*29*28*27*26*25*24*23*22*21*20*19)/(1*2*3*4*5*6*7*8*9*10*11*12)}}} = 86493225.    <U>ANSWER</U>
</pre>


Part (b)


<pre>
A committee of 18 board members, which includes 7 females, should include  18-7 = 11 males.


7 females from 13 females can be chosen in  {{{C[13]^7}}} = 1716 different ways.

11 males  from 17   males can be chosen in  {{{C[17]^11}}} = 12376 different ways.


Combining these different teams, consisting of 11 males and 7 females, 

we have 1716*12376 = 21237216 different ways to make such a committee which is required in part (b).
</pre>

Solved.


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This problem is on COMBINATIONS.


On 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>

&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.