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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can the letters of the word PERMUTATIONS be arranged if the}\hspace{.33em}\\~\\ & \normalsize \text{ (i) vowels are all together }\hspace{.33em}\\~\\ & \normalsize \text{ (ii) there are always 4 letters between P and S.}\hspace{.33em}\\~\\ \end{align}}\)

  2. rational
    • one year ago
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    How many vowels are there ?

  3. mathmath333
    • one year ago
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    all vowels are there

  4. rational
    • one year ago
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    put them in a bag and call it \(\phi\)

  5. rational
    • one year ago
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    how many ways can arrange the objects \(\{\phi, ~P, ~R, ~M,~T,~T,~N,~S\}\) ?

  6. mathmath333
    • one year ago
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    =(8/2)!

  7. anonymous
    • one year ago
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    12!/(12-5)! for i?

  8. rational
    • one year ago
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    you mean 8!/2 ?

  9. mathmath333
    • one year ago
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    ya this one

  10. rational
    • one year ago
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    Yes, next unpack the bag, how many ways can you arrange 5 vowels ?

  11. mathmath333
    • one year ago
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    can vowels be repeated

  12. rational
    • one year ago
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    what letters do you have in the bag ?

  13. mathmath333
    • one year ago
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    aeiou

  14. rational
    • one year ago
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    they all are distinct, how many ways can you arrange them ?

  15. mathmath333
    • one year ago
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    5!

  16. rational
    • one year ago
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    Yes, so the final answer is ?

  17. mathmath333
    • one year ago
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    8!*5!/2

  18. rational
    • one year ago
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    looks good!

  19. mathmath333
    • one year ago
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    ok the next one

  20. ikram002p
    • one year ago
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    separated than the first condition ?

  21. mathmath333
    • one year ago
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    P and S are at distance of 4 places always

  22. rational
    • one year ago
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    First find the number of ways of placing \(P, S\) : |dw:1439069671413:dw|

  23. mathmath333
    • one year ago
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    12*11

  24. rational
    • one year ago
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    nope, try again

  25. mathmath333
    • one year ago
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    11

  26. rational
    • one year ago
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    |dw:1439070002368:dw|

  27. rational
    • one year ago
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    If one letter of {P, S} is at index 1, where can the other letter be ?

  28. mathmath333
    • one year ago
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    6

  29. rational
    • one year ago
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    Yes, {P, S} can be mapped to {1, 6}

  30. rational
    • one year ago
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    By sliding to right, you can see that {P, S} can take on locations : {1, 6} {2, 7} {3, 8} {4, 9} {5, 10} {6, 11} {7, 12} how many are they ?

  31. mathmath333
    • one year ago
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    7

  32. rational
    • one year ago
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    and you can swap the locations, so there are 7*2 = 14 different ways to arrange {P, S}

  33. rational
    • one year ago
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    Next, arrange remaining 10 letters

  34. mathmath333
    • one year ago
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    10!/2

  35. rational
    • one year ago
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    Yes, so total num of permutations = 14(10!/2)

  36. mathmath333
    • one year ago
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    if the restriction of 4 places is not there then their are 10!/2 ways and the restrictions are their then there are 14*10!/2 ways but as the restrictions are more the the number of ways should decrease .

  37. rational
    • one year ago
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    if the restriction is not there, then there are 12!/2 different permutations not 10!/2

  38. mathmath333
    • one year ago
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    ohk i see the difference :D

  39. mathmath333
    • one year ago
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    hmm this little silly doubts make my brain spin

  40. rational
    • one year ago
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    its natural, my brain spins too :)

  41. rational
    • one year ago
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    listing the possibilities and looking at the problem from alternative ways usually helps...

  42. mathmath333
    • one year ago
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    but in the way of learning its essential to get rid of the small doubts

  43. rational
    • one year ago
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    haha! its good to ask questions there is an old saying : "there are no stupid questions, only stupid answers" remember that when asking a question which you feel is small/silly ;p

  44. mathmath333
    • one year ago
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    yes thumbs up!

  45. mathmath333
    • one year ago
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    remembering school days where teachers used to run after students after student asked questions

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