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Find the probability of selecting 5 science books and 3 math books from 7 science books and 14 math books.
The books are selected at random.
find p(5 science and 3 math)
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As posted, the problem formulation is INCORRECT.
The correct formulation is AS FOLLOWS:
8 books are selecting at random from the set of 7 Science books and 14 Math books.
Find the probability to get 5 Science books and 3 Math books.
SOLUTION
The number of favorable cases is . = . = 21*364 = 7644.
The total number of selections 5+3 = 8 books from the set of 7+14 = 21 books is
= combin(21,8) = 203490.
// combin is the standard Excel function to compute the number of COMBINATIONS,
which I use to facilitate my calculations.
The probability under the problem's question is the ratio of these two numbers
P = = = 0.03756 (rounded). ANSWER
Solved.
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This problem is on COMBINATIONS --- PLUS --- the Fundamental counting principle.
To learn more about these subjects, see the lessons
- Introduction to Combinations
- PROOF of the formula on the number of Combinations
- Problems on Combinations
- Fundamental counting principle problems
- 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.
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Don't you think that it is just a time to express your "THANKS" to me for my teaching ?
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I attentively observe / (look at) all your relevant posts.
I distinctively see your attempts to create your own problem,
and I distinctively see that you have no enough skills/knowledge to do it correctly.