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Math Help - permutation

  1. #1
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    permutation

    there were 15 english books ,9 spanish books,17 french books on a shelf.How many ways can you pick two books without them being the same.
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  2. #2
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    Hello, kingfahad!

    There are 15 English books, 9 Spanish books, 17 French books on a shelf.
    In how many ways can you pick two books without them being the same?

    \begin{array}{cccc}\text{Ways to pick one English and one Spanish:} & 15\cdot9 &=& 135 \\<br />
\text{Ways to pick one Spanish and one French:} & 9 \cdot 17 &=& 153 \\<br />
\text{Ways to pick one English and one French:} & 15\cdot17 &=& 255 \end{array}

    Answer: . 135 + 153 + 255 \;=\;\boxed{543} ways to get two different languages.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Check

    There are: . {41\choose2} \:=\:820 possible choices of two books.


    \begin{array}{ccccc}\text{There are:} &{15\choose2} &=& 105 &\text{ways to get 2 English books} \\ \\[-3mm]<br />
\text{There are:}& {9\choose2} &=& 36 & \text{ways to get 2 Spanish books} \\ \\[-3mm]<br />
\text{There are:} & {17\choose2} &=& 136 & \text{ways to get 2 French books} \end{array}


    Hence, there are: . 105 + 36 + 136 \:=\:277 ways to get the same language.


    Therefore, there are: . 820 - 277 \:=\:\boxed{543} ways to get different languages.



    By the way, these are not permuations.
    .
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