Question 1169264
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On my bookshelf I have 5 books of poetry, 15 graphic novels, 8 biographies and 3 self-help books. 
I plan to take 7 books with me on my vacation.
a)In how many different ways can I take 7 books with me on my vacation?

b)In how many different ways can my 7 books consist of 2 books of poetry, 3 graphic novels and 2 self-help books?
c)In how many different ways can my 7 books consist of exactly 3 graphic novels?
d)In how many different ways can my 7 books consist of at least 6 biographies?
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(b)  In how many different ways can my 7 books consist of 2 books of poetry, 3 graphic novels and 2 self-help books?


     You can select 2 books of poetry from  5 books of poetry by {{{C[5]^2}}} = {{{(5*4)/(1*2)}}} = 10 ways.


     You can select 3 graphic novels  from 15 graphic novels  by {{{C[15]^3}}} = {{{(15*14*13)/(1*2*3)}}} = 455 ways.


     You can select 2 self-help books  from 3 self-help books  by {{{C[3]^2}}} = {{{(3*2)/(1*2)}}} = 3 ways.


     Since these selections are INDEPENDENT in separate categories, the total number of choices is the product 10*455*3 = 13650,

        according to the <U>foundamental counting principle</U>.
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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/Fundamental-counting-principle-problems.lesson>Fundamental counting principle problems</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.