Question 1203031
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If 3 books are picked from the shelf containing 5 novels, 3 books of poems and a dictionary, then
(1) what is the prbability that the dictionary is selected.
(2) 2 novels and 1 book of poem are selected
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<pre>
(1) The number of all possible triples of books is  

        total = {{{C[5+3+1]^3}}} = {{{C[9]^3}}} = {{{(9*8*7)/(1*2*3)}}} = 84.


    The number of all favorable triples is

        favorable = {{{C[1]^1*C[5+3]^2}}} = {{{C[8]^2}}} = {{{(8*7)/2}}} = 4*7 = 28.


    THEREFORE, the answer to question (1) is

        P = {{{favorable/total}}} = {{{28/84}}} = {{{1/3}}}.



(2)  Having the number of total triples just calculated in (a) as 84,
     we only need to calculate the number of favorable triples, which in this case is

        favorable = {{{C[5]^2*C[3]^1}}} = {{{((5*2)/(1*2))*3}}} = 5*3 = 15.


    THEREFORE, the answer to question (2) is

        P = {{{favorable/total}}} = {{{15/84}}} = {{{5/28}}}.
</pre>

Solved.


Since in this problem the order of selected books does not matter,
we use COMBINATIONS to calculate the number of total triples and favorable triples.


On &nbsp;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>

in this site.