Question 1103356
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<pre>
Let me solve  <U>MORE SIMPLE</U>  problem for you.



     6 freshmen  and  8 sophomores are eligible to be on a committee. 

     If a committee of 5 students is chosen at random, what is the probability that it is made up of 3 freshmen and 2 sophomores? 



In all, there are 6 + 8 = 14 students to choose from.

So, there are {{{C[14]^5}}} ways to made the committee of 5 students. 

It is your  <U>TOTAL space</U>  of events,  and it has  {{{(14*13*12*11*10)/(1*2*3*4*5)}}} = 2002 elements in all.


Next, in how many ways can you choose 3 freshmen   of 6 ?   - In {{{C[6]^3}}} = {{{(6*5*4)/(1*2*3)}}} = 20 ways.

      In how many ways can you choose 2 sophomores of 8 ?   - In {{{C[8]^2}}} = {{{(8*7)/(1*2)}}} = 28 ways.


Thus   there are {{{C[6]^3}}}.{{{C[8]^2}}} = 20*28 = 560 ways to form the committee in accordance with the given requirements.


So, the probability under the question is  P = {{{560/2002}}}.


Or, if you want to have it as a "formula",  P = {{{(C[6]^3*C[8]^2)/C[6+8]^(3+2)}}}.
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On combinations, 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.