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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{A student is allowed to select at most n books } \hspace{.33em}\\~\\ & \normalsize \text{from a collection of (2n+1) books. if the total number } \hspace{.33em}\\~\\ & \normalsize \text{of ways in which he can select at least one book is 63.find n} \hspace{.33em}\\~\\ & a.)\ 4 \hspace{.33em}\\~\\ & b.)\ 3 \hspace{.33em}\\~\\ & c.)\ 5 \hspace{.33em}\\~\\ & d.)\ 6 \hspace{.33em}\\~\\ \end{align}}\)

  2. triciaal
    • one year ago
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    |dw:1440601651278:dw|

  3. triciaal
    • one year ago
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    @Nnesha can you help with this?

  4. ganeshie8
    • one year ago
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    you want to solve for \(n\) in : \[2^n-1 = 63\]

  5. mathmath333
    • one year ago
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    is the answer 6

  6. ganeshie8
    • one year ago
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    no wait, they made it tricky

  7. ganeshie8
    • one year ago
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    lets do it step by step

  8. mathmath333
    • one year ago
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    here is one of the link i didnt understand the answer given http://www.meritnation.com/ask-answer/question/a-student-is-allowed-to-select-at-most-n-books-from-a-colle/sets/2913008

  9. ganeshie8
    • one year ago
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    forget that link, it would be easy if u try it on ur own

  10. ganeshie8
    • one year ago
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    how good are u with pascal triangle ?

  11. mathmath333
    • one year ago
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    i just only know how to form a pascal triangle 1 121 1331...

  12. ganeshie8
    • one year ago
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    lets review one important result of pascal triangle quick

  13. ganeshie8
    • one year ago
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    ``` 1 11 121 1331... ``` add the entries in first row, you get : 1 = 1 = 2^0 add the entries in second row, you get : 1+1 = 2 = 2^1 add the entries in third row, you get : 1+2+1 = 4 = 2^2

  14. ganeshie8
    • one year ago
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    see the pattern ?

  15. mathmath333
    • one year ago
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    yes

  16. ganeshie8
    • one year ago
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    can you guess the sum of entries in 100000th row ?

  17. mathmath333
    • one year ago
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    \(2^{99999}\) ?

  18. ganeshie8
    • one year ago
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    Yes, but that looks ugly to have different numbers for index and exponent we can fix it easily, if we say that we start counting the rows from "0"

  19. Astrophysics
    • one year ago
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    .

  20. ganeshie8
    • one year ago
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    |dw:1440602644567:dw|

  21. mathmath333
    • one year ago
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    i didnt understand , do u mean i need to start couting from second row

  22. ganeshie8
    • one year ago
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    now we can say that the sum of entries in \(n\)th row is \(2^n\)

  23. mathmath333
    • one year ago
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    ok if we count from the second row as row 1

  24. ganeshie8
    • one year ago
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    Exactly, in other words we're starting our count for rows from 0,1,2,...

  25. ganeshie8
    • one year ago
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    instead of 1,2,3,...

  26. mathmath333
    • one year ago
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    ok

  27. ganeshie8
    • one year ago
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    so when somebody asks you to look at "3"rd row of pascal triangle, they really mean the 4th row ok

  28. mathmath333
    • one year ago
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    yes i get that.

  29. ganeshie8
    • one year ago
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    can you tell me the sum of entries in row 6 and also the sum of entries in row 7 |dw:1440602907133:dw|

  30. mathmath333
    • one year ago
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    sum of 6th row =\(2^{6}\) sum of 7th row =\(2^{7}\)

  31. ganeshie8
    • one year ago
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    good, how is pascal triangle related to combinations/counting ?

  32. mathmath333
    • one year ago
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    i don't knw

  33. ganeshie8
    • one year ago
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    suppose you have \(6\) objects how many total ways are there to choose 2 out of them ?

  34. mathmath333
    • one year ago
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    6C2

  35. ganeshie8
    • one year ago
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    simplify, what is the number

  36. mathmath333
    • one year ago
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    15

  37. ganeshie8
    • one year ago
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    Yes, now look at the 6th row in pascal triangle : |dw:1440603215894:dw|

  38. ganeshie8
    • one year ago
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    suppose you have \(6\) objects how many total ways are there to choose 3 out of them ?

  39. mathmath333
    • one year ago
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    20

  40. ganeshie8
    • one year ago
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    you can guess, it is there in pascal triangle : |dw:1440603390646:dw|

  41. mathmath333
    • one year ago
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    yes

  42. ganeshie8
    • one year ago
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    \(\large \binom{6}{4}\) is the number locatd at 4th position in 6th row (we count from 0)

  43. ganeshie8
    • one year ago
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    using pascal's triangle, can you tell the value of \(\dbinom{7}{5}\) ?

  44. mathmath333
    • one year ago
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    yes it is same as \(\binom{6}{2}=\binom{6}{4}\)

  45. ganeshie8
    • one year ago
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    Yes, it has that symmtry the values in left half are same as the values in right half

  46. mathmath333
    • one year ago
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    7th row 5th number or 2nd number

  47. ganeshie8
    • one year ago
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    what is it

  48. ganeshie8
    • one year ago
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    can you highlight the number

  49. mathmath333
    • one year ago
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    sry it was sry it was 3ed number 21

  50. ganeshie8
    • one year ago
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    \(\dbinom{7}{5}\) is the 5th element in 7th row : |dw:1440603778591:dw|

  51. ganeshie8
    • one year ago
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    so basically you want to solve : \[\large \dfrac{2^{2n+1}}{2}-1 = 63\]

  52. mathmath333
    • one year ago
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    yea u told that

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