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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{Find the number of ways in which the letters of the word MACHINE }\hspace{.33em}\\~\\ & \normalsize \text{can be arranged so that the vowels may occupy only odd positions. }\hspace{.33em}\\~\\ & a.)\ 4!\times 4! \hspace{.33em}\\~\\ & b.)\ ^{7}P_{3}\times 4! \hspace{.33em}\\~\\ & c.)\ ^{7}P_{4}\times 3! \hspace{.33em}\\~\\ & d.)\ \text{none of these} \hspace{.33em}\\~\\ \end{align}}\)

  2. ganeshie8
    • one year ago
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    |dw:1440622392209:dw|

  3. ganeshie8
    • one year ago
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    How many positions are there for the vowels to go to ?

  4. mathmath333
    • one year ago
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    4 position for vowels

  5. ganeshie8
    • one year ago
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    how many vowels are there ?

  6. mathmath333
    • one year ago
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    |dw:1440622528962:dw|

  7. mathmath333
    • one year ago
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    3 vowels

  8. ganeshie8
    • one year ago
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    4 positions 3 vowels first vowel can go into any one of the 4 positions : 4 ways after that, second vowel can go into any one of the remaining 3 positions : 3 ways after that, the third vowel can go into any one of the remaining 2 positions : 2 ways so total ways of arranging 3 vowels into 4 positions is 4*3*2

  9. ganeshie8
    • one year ago
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    we're done with vowels, next look at rest of the word

  10. mathmath333
    • one year ago
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    can u apply formula for that 4 positions 3 vowels

  11. ganeshie8
    • one year ago
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    sure, what formula ?

  12. mathmath333
    • one year ago
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    Permutation

  13. ganeshie8
    • one year ago
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    yes it is the permutation formula : \(4P3\) i just elaborated for you

  14. mathmath333
    • one year ago
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    ohk

  15. ganeshie8
    • one year ago
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    what about the consonants

  16. mathmath333
    • one year ago
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    3 positions 4 cnsonants

  17. ganeshie8
    • one year ago
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    really ? we have just used 3 positions for vowels right

  18. ganeshie8
    • one year ago
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    after placing 3 vowels, we see 4 empty positions, yes ?

  19. mathmath333
    • one year ago
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    |dw:1440623136170:dw|

  20. ganeshie8
    • one year ago
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    there are no restrictions on consonants they can go into odd positions that are not occupied by vowels too

  21. ganeshie8
    • one year ago
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    there are 3 even positions but there are 4 "empty" positions

  22. mathmath333
    • one year ago
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    sry 4 positions

  23. ganeshie8
    • one year ago
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    Yes 4 positions 4 consonants how many permutations ?

  24. mathmath333
    • one year ago
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    4!

  25. ganeshie8
    • one year ago
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    Yes

  26. mathmath333
    • one year ago
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    is option a.) correct

  27. ganeshie8
    • one year ago
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    you can arrange vowels in 4*3*2 ways and for each of that arrangement, you can arrange consonants in 4! ways so total arrangements is ?

  28. mathmath333
    • one year ago
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    4!*4!

  29. ganeshie8
    • one year ago
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    looks good!

  30. mathmath333
    • one year ago
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    thnks

  31. perl
    • one year ago
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    *

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