Question 1157923: 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
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
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.
The correct question (and the ONLY / UNIQUE question), which suits to the given situation, is
How many described selections are possible ?
It is the only reasonable question, which suits to the context.
SOLUTION
You can select 4 science books from 9 science books by  =  = 126 ways.
You can select 5 math books from 10 math books by  =  = 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. ANSWER
Solved.
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This problem is for COMBINATIONS.
On Combinations, see introductory 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.
/\/\/\/\/\/\/\/
Regarding your DEFECTIVE formulation in the post,
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".
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
I think saying the statement of the problem is incorrect is a bit harsh. I do think that the problem is presented poorly.
By implication, the problem really asks the probability if, WHEN 9 BOOKS ARE SELECTED FROM 9 science books and 10 math books, 4 science books and 5 math books are selected.
P(4 science and 5 math) = 
Of course simplify the fraction or express as a decimal if needed.
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