Question 1115051
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It is very simple problem.   Much simpler than you,  probably,  thought at the beginning.
Your major task is to read the condition attentively to maximally simplify it.


<pre>
The total number of balls in the bag was initially 4 + 3 + 2 + 1 = 10.

How many ways are there to grab 8 balls from 10 ?  - There are  {{{C[10]^8}}} = {{{10!/(8!*2!)}}} = {{{(10*9)/(1*2)}}} = 45 ways.

    It is the full space of events.



In how many ways she may have 4 red balls among those 8 she grabbed? - In  {{{C[6]^4}}} = {{{6!/(4!*2!)}}} = {{{(6*5)/(1*2)}}} = 15 ways.

    (just having 4 red, she can complement them by 4 other balls, choosing them arbitrary among 6 remaining balls).



So, the probability under the question is  {{{15/45}}} = {{{1/3}}} = 33.33%
</pre>

Solved.


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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.