SOLUTION: There are nine female board members and twenty-one male board members. How many ways are there to make a committee of twelve board members if exactly two must be female? Dete

Question 1136801: There are nine female board members and twenty-one male board members.
How many ways are there to make a committee of twelve board members if exactly two must be female?
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.
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~~~~~

(a)  You can select 2 females of 9 females by   =  = 36 ways.


     You can select 12-2 = 10 males of 21 males by   =  =  ways = 352716 ways.


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


      .  = 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   :


     P =  = .


I leave it to you to calculate the number  and to complete this assignment. It is just pure mechanical work.

Happy calculations !

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

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
in this site.

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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