Re: Binomial coefficient

Denis Feldmann wrote:

Han de Bruijn a écrit :

Denis Feldmann wrote:

Han de Bruijn a écrit :

desktop wrote:

In a book I am reading the Binomial coefficient is defined as:

(n k) = n^(k)/k! = n!/(k!*(n-k)!)

But if I try with this example:

(10 3)

I get, using "n^(k)/k!":

10^3/6 = 166.66666

Using "n!/(k!*(n-k)!)" I get:

10!/(3!*7!) = 120

But should the two equations not give the same result?

Not if the first one [ n^(k)/k! ] is simply wrong.

As usual;,you are extremely pertinent and useful. Did you notice that n^(k) is not written the same as n^k ? Could it be you are missing somrthing there (like the notation x^(k)=x(x-1)(x-2)...(x-k+1) )?

Something? As well as the OP, I've never seen this notation, indeed ..

Try reading a book or two, like "Concrete Mathematics" (Graham, Knuth, Patashnik) (ok, usually, as in those books, this is written x^"undescored k"). But anyway, I ibsist : when one reads 4^(3), he must suspect that this is not hte same as 4^3 (or see "Leibnitz formula" : f^(n) is tne n-th derivative of f, not the n-th power...)

Ah, I see: n^(k) is the k-th derivative of n. Thanks! :-)

And ab = a times b. Thus 43 = four times three and 1 1/2 = 1 times 1/2,
not 1 + 1/2. It may be all very confusing for a beginner in mathematics
(no kidding).

Han de Bruijn

.

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