Question 1136801
.
There are nine female board members and twenty-one male board members.

(a) How many ways are there to make a committee of twelve board members if exactly two must be female?

(b) Determine the probability of selecting a committee of twelve board members where exactly two of the members were female. 
Write your answer as a decimal, rounded to the nearest thousandth.
~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
(a)  You can select 2 females of 9 females by  {{{C[9]^2}}} = {{{(9*8)/2}}} = 36 ways.


     You can select 12-2 = 10 males of 21 males by  {{{C[21]^10}}} = {{{(21*20*19*18*17*16*15*14*13*12)/(1*2*3*4*5*6*7*8*9*10)}}} = {{{1279935820800
/3628800}}} ways = 352716 ways.


     The answer to question (a) is the product of these numbers


     {{{C[9]^2}}} . {{{C[21]^10}}} = 36 * 352716 = 12697776 ways.


(b)  To answer question (b), you need to divide the answer to question (a) by the number of all combinations 
     of 21 items taken 12 at a time  {{{C[21]^12}}} :


     P = {{{(C[9]^2 * C[21]^10)/ C[21]^12}}} = {{{12697776/C[21]^12}}}.


I leave it to you to calculate the number {{{C[21]^12}}} and to complete this assignment. It is just pure mechanical work.
</pre>

Happy calculations !


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


On Combinations, &nbsp;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>

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.