Question 1157923
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find the probaility of selecting 4 science books and 5 math books from 9 science books and 10 math books. The books are selected at random.


I am doing a study book for sat but i have never done these types of problems so i was wondering if i could get some help
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            Hello,  the question in this problem  (in your post)  is posed  INCORRECTLY.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The correct question &nbsp;(and the &nbsp;<U>ONLY / UNIQUE</U> &nbsp;question), &nbsp;which suits to the given situation, &nbsp;is


<pre>
               How many described selections are possible ?
</pre>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is the only reasonable question, &nbsp;which suits to the context.



<U>SOLUTION</U>


<pre>
You can select 4 science books from 9 science books by {{{C[9]^4}}} = {{{(9*8*7*6)/(1*2*3*4)}}} = 126 ways.


You can select 5 math books from 10 math books by {{{C[10]^5}}} = {{{(10*9*8*7*6)/(1*2*3*4*5)}}} = 252 ways.


In each category, the selections are independent --- therefore, according to the basic counting principle,

the total number of ways to make these selections is the product


        126*252 = 31752.    <U>ANSWER</U>
</pre>

Solved.


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This problem is for COMBINATIONS.


On Combinations, &nbsp;see introductory 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.



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Regarding your DEFECTIVE formulation in the post,

<pre>
    we at this forum receive HUGE amount of such defective formulations.

    So huge, that I think sometimes, where, from which GARBAGE BOXES these visitors

    recover their "problems".
</pre>