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Thread: Counting question

  1. #1
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    Question Counting question

    I have two set of solutions, which one has answered the question correctly?

    Counting question-m1.png
    Solution 1:
    Counting question-m1.1.png
    Solution 2:
    Counting question-m1.2.jpg
    Please correct where wrong if both are wrong, thanks
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  2. #2
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    Re: Counting question

    Quote Originally Posted by inayat View Post
    I have two set of solutions, which one has answered the question correctly?
    Please correct where wrong if both are wrong, thanks
    Forgive me, but I find your handwriting almost impossible to read.
    Can you please type the post?
    Thanks from topsquark
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  3. #3
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    Re: Counting question

    Quote Originally Posted by Plato View Post
    Forgive me, but I find your handwriting almost impossible to read.
    Can you please type the post?
    Solution 1:

    Order matters since sequence 0,1,2,3,4 is different from 1,0,2,3,4
    Repetition is allowed since we are not given explicitly that repetition is not allowed

    a) No. of sequences = 16^5
    b) No. of sequence = p(16,6) = 16!/10!= 16x14x15x14x13x12x11
    c) No. of sequence = total sequence - (no. of sequence having all numbers - no. of sequence having all letters)
    = 16^5 - 10^5 -6^5

    Solution 2 should be readable

    Please let me know which one is correct or how it should be answered where wrong.

    Thanks
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  4. #4
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    Re: Counting question

    Quote Originally Posted by inayat View Post
    Solution 2 should be readable
    Ya ya...I'm sure YOU can read it...
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    Re: Counting question

    Quote Originally Posted by DenisB View Post
    Ya ya...I'm sure YOU can read it...
    Lol excuse me?
    It is though xD
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  6. #6
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    Re: Counting question

    Quote Originally Posted by inayat View Post
    Solution 1:

    Order matters since sequence 0,1,2,3,4 is different from 1,0,2,3,4
    Repetition is allowed since we are not given explicitly that repetition is not allowed

    a) No. of sequences = 16^5
    b) No. of sequence = p(16,6) = 16!/10!= 16x14x15x14x13x12x11
    c) No. of sequence = total sequence - (no. of sequence having all numbers - no. of sequence having all letters)
    = 16^5 - 10^5 -6^5
    All of those answers are correct.

    What is the question that goes with solution #2?
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  7. #7
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    Re: Counting question

    Quote Originally Posted by Plato View Post
    All of those answers are correct.

    What is the question that goes with solution #2?
    Its my friends working out for the same question and i want to know whether his is right and if not, why.
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  8. #8
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    Re: Counting question

    Quote Originally Posted by inayat View Post
    Its my friends working out for the same question and i want to know whether his is right and if not, why.
    Again I cannot read your writing. You seen to have a good grasp on parts a) & b)!

    for part c) "at least one of each"
    There are $\large{10^5+6^5}$ strings of either all digits or all letters. Subtract that from the total to get at least one of each.
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  9. #9
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    Re: Counting question

    Quote Originally Posted by Plato View Post
    Again I cannot read your writing. You seen to have a good grasp on parts a) & b)!

    for part c) "at least one of each"
    There are $\large{10^5+6^5}$ strings of either all digits or all letters. Subtract that from the total to get at least one of each.
    For part b)

    Would it be 16!/11! or 16!/10! ?
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  10. #10
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    Re: Counting question

    Quote Originally Posted by inayat View Post
    For part b)
    Would it be 16!/11! or 16!/10! ?
    Do you understand that a permutation of $n$ taken $k,~0\le k\le n$ at a time is $\large{^n\mathcal{P}_k=\dfrac{n!}{(n-k)!}}~?$

    The correct answer for (b) is $\large{^{16}\mathcal{P}_5}$
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