what is the probability that the letters e, g, and k are all in the same subset?












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the 26 letters of the alphabet are to be randomly partitioned into subsets with 5,10, and 11 letters respectively. what is the probability that the letters e, g, and k are all in the same subset?
I am unsure about how to go about this. I have tried 3!/5!10!11! And I know that is not it and have also tried (5C3)(10C3)(11C3)/(26C3) and that isnt correst either. I just need a push in the right direction










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  • $begingroup$
    Do you know how to count the ways of splitting 26 letters into subsets of sizes 5,10, and 11?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:46










  • $begingroup$
    Once you’ve done that you can break it into three cases: egk are in the subset of size 5,10, or 11. How many ways are there for each case to happen?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:49










  • $begingroup$
    This helps a lot, thank you!
    $endgroup$
    – Court
    Dec 9 '18 at 14:51






  • 1




    $begingroup$
    I’m glad! You should write the answer yourself down below once you solve it :)
    $endgroup$
    – Ben
    Dec 9 '18 at 15:01
















0












$begingroup$


the 26 letters of the alphabet are to be randomly partitioned into subsets with 5,10, and 11 letters respectively. what is the probability that the letters e, g, and k are all in the same subset?
I am unsure about how to go about this. I have tried 3!/5!10!11! And I know that is not it and have also tried (5C3)(10C3)(11C3)/(26C3) and that isnt correst either. I just need a push in the right direction










share|cite|improve this question









$endgroup$












  • $begingroup$
    Do you know how to count the ways of splitting 26 letters into subsets of sizes 5,10, and 11?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:46










  • $begingroup$
    Once you’ve done that you can break it into three cases: egk are in the subset of size 5,10, or 11. How many ways are there for each case to happen?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:49










  • $begingroup$
    This helps a lot, thank you!
    $endgroup$
    – Court
    Dec 9 '18 at 14:51






  • 1




    $begingroup$
    I’m glad! You should write the answer yourself down below once you solve it :)
    $endgroup$
    – Ben
    Dec 9 '18 at 15:01














0












0








0


0



$begingroup$


the 26 letters of the alphabet are to be randomly partitioned into subsets with 5,10, and 11 letters respectively. what is the probability that the letters e, g, and k are all in the same subset?
I am unsure about how to go about this. I have tried 3!/5!10!11! And I know that is not it and have also tried (5C3)(10C3)(11C3)/(26C3) and that isnt correst either. I just need a push in the right direction










share|cite|improve this question









$endgroup$




the 26 letters of the alphabet are to be randomly partitioned into subsets with 5,10, and 11 letters respectively. what is the probability that the letters e, g, and k are all in the same subset?
I am unsure about how to go about this. I have tried 3!/5!10!11! And I know that is not it and have also tried (5C3)(10C3)(11C3)/(26C3) and that isnt correst either. I just need a push in the right direction







probability






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share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 9 '18 at 14:42









CourtCourt

1




1












  • $begingroup$
    Do you know how to count the ways of splitting 26 letters into subsets of sizes 5,10, and 11?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:46










  • $begingroup$
    Once you’ve done that you can break it into three cases: egk are in the subset of size 5,10, or 11. How many ways are there for each case to happen?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:49










  • $begingroup$
    This helps a lot, thank you!
    $endgroup$
    – Court
    Dec 9 '18 at 14:51






  • 1




    $begingroup$
    I’m glad! You should write the answer yourself down below once you solve it :)
    $endgroup$
    – Ben
    Dec 9 '18 at 15:01


















  • $begingroup$
    Do you know how to count the ways of splitting 26 letters into subsets of sizes 5,10, and 11?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:46










  • $begingroup$
    Once you’ve done that you can break it into three cases: egk are in the subset of size 5,10, or 11. How many ways are there for each case to happen?
    $endgroup$
    – Ben
    Dec 9 '18 at 14:49










  • $begingroup$
    This helps a lot, thank you!
    $endgroup$
    – Court
    Dec 9 '18 at 14:51






  • 1




    $begingroup$
    I’m glad! You should write the answer yourself down below once you solve it :)
    $endgroup$
    – Ben
    Dec 9 '18 at 15:01
















$begingroup$
Do you know how to count the ways of splitting 26 letters into subsets of sizes 5,10, and 11?
$endgroup$
– Ben
Dec 9 '18 at 14:46




$begingroup$
Do you know how to count the ways of splitting 26 letters into subsets of sizes 5,10, and 11?
$endgroup$
– Ben
Dec 9 '18 at 14:46












$begingroup$
Once you’ve done that you can break it into three cases: egk are in the subset of size 5,10, or 11. How many ways are there for each case to happen?
$endgroup$
– Ben
Dec 9 '18 at 14:49




$begingroup$
Once you’ve done that you can break it into three cases: egk are in the subset of size 5,10, or 11. How many ways are there for each case to happen?
$endgroup$
– Ben
Dec 9 '18 at 14:49












$begingroup$
This helps a lot, thank you!
$endgroup$
– Court
Dec 9 '18 at 14:51




$begingroup$
This helps a lot, thank you!
$endgroup$
– Court
Dec 9 '18 at 14:51




1




1




$begingroup$
I’m glad! You should write the answer yourself down below once you solve it :)
$endgroup$
– Ben
Dec 9 '18 at 15:01




$begingroup$
I’m glad! You should write the answer yourself down below once you solve it :)
$endgroup$
– Ben
Dec 9 '18 at 15:01










1 Answer
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$begingroup$

Hint:



If $S$ is a randomly chosen subset of ${text{a,b,}cdotstext{,z}}$ having $n$ elements then:



$P(text{e}in Swedgetext{g}in Swedgetext{k}in S)=P(text{e}in S)P(text{g}in Smidtext{e}in S)P(text{k}in Smidtext{g}in Swedgetext{e}in S)=frac{n}{26}frac{n-1}{25}frac{n-2}{24}$






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    1 Answer
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    1 Answer
    1






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    active

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    active

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    0












    $begingroup$

    Hint:



    If $S$ is a randomly chosen subset of ${text{a,b,}cdotstext{,z}}$ having $n$ elements then:



    $P(text{e}in Swedgetext{g}in Swedgetext{k}in S)=P(text{e}in S)P(text{g}in Smidtext{e}in S)P(text{k}in Smidtext{g}in Swedgetext{e}in S)=frac{n}{26}frac{n-1}{25}frac{n-2}{24}$






    share|cite|improve this answer









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      0












      $begingroup$

      Hint:



      If $S$ is a randomly chosen subset of ${text{a,b,}cdotstext{,z}}$ having $n$ elements then:



      $P(text{e}in Swedgetext{g}in Swedgetext{k}in S)=P(text{e}in S)P(text{g}in Smidtext{e}in S)P(text{k}in Smidtext{g}in Swedgetext{e}in S)=frac{n}{26}frac{n-1}{25}frac{n-2}{24}$






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        Hint:



        If $S$ is a randomly chosen subset of ${text{a,b,}cdotstext{,z}}$ having $n$ elements then:



        $P(text{e}in Swedgetext{g}in Swedgetext{k}in S)=P(text{e}in S)P(text{g}in Smidtext{e}in S)P(text{k}in Smidtext{g}in Swedgetext{e}in S)=frac{n}{26}frac{n-1}{25}frac{n-2}{24}$






        share|cite|improve this answer









        $endgroup$



        Hint:



        If $S$ is a randomly chosen subset of ${text{a,b,}cdotstext{,z}}$ having $n$ elements then:



        $P(text{e}in Swedgetext{g}in Swedgetext{k}in S)=P(text{e}in S)P(text{g}in Smidtext{e}in S)P(text{k}in Smidtext{g}in Swedgetext{e}in S)=frac{n}{26}frac{n-1}{25}frac{n-2}{24}$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 9 '18 at 15:14









        drhabdrhab

        100k544130




        100k544130






























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