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Heads or tails? (Question from Feynman lectures)

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  1. Sep 5, 2015 #1
    I have been going through feynmans lectures on probability and have a few questions that i can't answer ; in the part regarding fluctuations he introduces us to tree diagrams(pascals triangle ) and gives an example regarding the toss of a coin
    If we consider the no. Of tosses as n and no. Of heads as k then it can be given as
    ( n) n!
    ( k ) = ----
    k!(n-k)!

    I know that n! Represents n factorial and the fact that probability is generally
    Given by
    Probability = highest estimate of an event
    ----------------------------
    Total no. Of events
    However what i dont get is why do we multiply k! By (n-k)! Souldnt it be n! In the denominator and k! In the numerator ?
    I know it has something to do with the triangle however unable to figure it out
     
  2. jcsd
  3. Sep 5, 2015 #2
    The equation is (n)= n!
    (k) -----
    k!(
     
  4. Sep 5, 2015 #3
    The equation is (n)= n!
    -----
    k!(n-k)!
     
  5. Sep 5, 2015 #4

    PeroK

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    Science Advisor
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    Gold Member

    You're actually asking, I think, about how many ways you can get ##k## heads from ##n## coin tosses. And why the answer is ##\frac{n!}{(n-k)! k!}##

    You could start by taking ##n = 5##, say, and counting all the ways you can get ##k = 0, 1, 2, 3, 4## and ##5##.

    Then see whether that fits the formula, and why.
     
  6. Sep 6, 2015 #5
    BTW (just in case anyone is interested), this was not Feynman's lecture, but Matt Sands' lecture. Feynman had to go out of town on some business for a week, so Matt Sands gave the lectures that became FLP Vol. I Chapters 5 and 6.
     
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