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mathmath333

  • one year ago

Counting Problem

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{How many words of 11 letters could be formed with } \hspace{.33em}\\~\\ & \normalsize \text{all the vowels present in even places, using all the } \hspace{.33em}\\~\\ & \normalsize \text{letters of the alphabet ?(without repetition) } \hspace{.33em}\\~\\ \end{align}}\)

  2. hartnn
    • one year ago
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    what are your thoughts?

  3. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & a.)\ ^{21}P_{6}\times 5! \hspace{.33em}\\~\\ & b.)\ 21! \hspace{.33em}\\~\\ & c.)\ ^{21}P_{5}\times 5! \hspace{.33em}\\~\\ & d.)\ ^{26}P_{8} \hspace{.33em}\\~\\ \end{align}}\)

  4. mathmath333
    • one year ago
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    |dw:1440438880520:dw|

  5. mathmath333
    • one year ago
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    i m confused on how to think here

  6. hartnn
    • one year ago
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    those 5 places are blocked with 5 vowels, which can be arranged among themselves in how many ways??

  7. mathmath333
    • one year ago
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    6 letters should be vowels and 5 letters non vowels

  8. hartnn
    • one year ago
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    how many other letters are left? in how many ways can you arrange those other letters in 6 places?

  9. hartnn
    • one year ago
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    5 vowels, at places: 2,4,6,8,10

  10. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & ^{6}P_{5}\ ways \hspace{.33em}\\~\\ \end{align}}\)

  11. mathmath333
    • one year ago
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    iis it correct

  12. hartnn
    • one year ago
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    sorry for asking many questions at one time. lets just concentrate on 5 places are blocked with 5 vowels, which can be arranged among themselves in how many ways??

  13. mathmath333
    • one year ago
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    5! ways

  14. hartnn
    • one year ago
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    good! now forget about those 5 places, they are done only 6 more places to go, and how many options do we have? hint : consonants

  15. mathmath333
    • one year ago
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    there are 6 places and 21 consonants remaining

  16. hartnn
    • one year ago
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    and how can we arrange that?

  17. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & ^{21}P_{6}\ ways \hspace{.33em}\\~\\ \end{align}}\)

  18. hartnn
    • one year ago
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    \(\huge \checkmark \)

  19. hartnn
    • one year ago
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    any more doubts? :)

  20. hartnn
    • one year ago
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    yes

  21. mathmath333
    • one year ago
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    does u mean 1st option is correct

  22. mathmath333
    • one year ago
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    ok thanks

  23. hartnn
    • one year ago
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    yes. clear any doubts that you have in your mind ...

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