Question 1116838
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All possible opportunities are listed in the table below (two most-left columns)


 #of fiction books   #of non-fiction books  #of combinations  value
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        1                     4              {{{C[7]^1*C[9]^4}}}            882
 
        2                     3              {{{C[7]^2*C[9]^3}}}           1764

        3                     2              {{{C[7]^3*C[9]^2}}}           1260

        4                     1              {{{C[7]^4*C[9]^1}}}            315



The third column contains the formulas for the number of selections.

The fourth column contains the values calculated with these formulas:


{{{C[7]^1*C[9]^4}}} = {{{7*((9*8*7*6)/(1*2*3*4))}}} = 882;

{{{C[7]^2*C[9]^3}}} = {{{((7*6)/(1*2))*((9*8*7)/(1*2*3))}}} = 1764;

{{{C[7]^3*C[9]^2}}} = {{{((7*6*5)/(1*2*3))*((9*8)/(1*2))}}} = 1260;

{{{C[7]^4*C[9]^1}}} = {{{((7*6*5)/(1*2*3))*9}}} = 315.


Now your last step is to add all four numbers in the right column:  882 + 1764 + 1260 + 315 = 4221.


<U>Answer</U>.  The selection of books can be made in 4221 ways.
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