Question 1119875
.
A bag contains 7 red marbles, 9 white marbles, and 9 blue marbles. You draw 5 marbles out at random, without replacement. 
What is the probability that all the marbles are red? 
What is the probability that exactly two of the marbles are red? 
What is the probability that none of the marbles are red?
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Notice that the total number of marbles is  7 + 9 + 9 = 25.


Therefore the expressions for probabilities in all  3  cases have    {{{C[25]^5}}}    as the denominator.


<pre>
(a)  What is the probability that all the marbles are red? 

     You can select 5 red marbles of 7 red marbles in  {{{C[7]^5}}} ways. Therefore the answer is  {{{C[7]^5/C[25]^5}}}.


(b)  What is the probability that exactly two of the marbles are red?

     You can select 2 red marbles of 7 red marbles in  {{{C[7]^2}}} ways.  Then you can add any 3 marbles of remaining 9+9 = 18 white and blue marbles.

     You can do it in {{{C[7]^2*C[18]^3}}} ways.  Therefore the answer is  {{{(C[7]^2*C[18]^3)/C[25]^5}}}  ways.



(c)  What is the probability that none of the marbles are red?

     It means that you select 5 marbles among 18 = 9 + 9 white and blue marbles.

     You can do it in  {{{C[18]^5}}} ways.  Therefore, the answer is  {{{C[18]^5/C[25]^5}}}.  
</pre>

Solved.


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In order for solve such problems with confidence and understand the solution, &nbsp;when it is presented to you, &nbsp;you should know the basics.


In this case, &nbsp;the basics is the info about Combinations.


On Combinations, &nbsp;read these 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.