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The Maxima on-line user's manual

Algebra Calculator

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Binomial Calculator

Binomial

Function: binomial (<x>, <y>) The binomial coefficient <x>!/(<y>! (<x> - <y>)!). If <x> and <y> are integers, then the numerical value of the binomial coefficient is computed. If <y>, or <x - y>, is an integer, the binomial coefficient is expressed as a polynomial.

load(distrib);
 n:10;
p:1/6;
versuche:1000 /* diese Anzahl sollte man variieren: 100,1000,10000,... die Ausführungsdauer steigt allerdings */;
anzahl_6:random_binomial(n,p,versuche);
load(descriptive);
gruppierung:discrete_freq(anzahl_6);
 X:gruppierung[1];
 H:gruppierung[2];
Verteilung: matrix( ["Anzahl der 6-er","Häufigkeit"],  [transpose(X),transpose(H)] );
plot2d([discrete, X, H]);
P:H/1000;
   emp:[discrete,X,P];
 plot2d(emp);
W(k):=binomial(n,k)*p**k*(1-p)**(n-k);
B:makelist(W(k),k,0,n);
 k:makelist(i,i,0,n);
liste:[discrete,k,B];
plot2d(liste);
plot2d(emp);

Examples:

          (%i1) binomial (11, 7);
          (%o1)                          330
          (%i2) 11! / 7! / (11 - 7)!;
          (%o2)                          330
          (%i3) binomial (x, 7);
                  (x - 6) (x - 5) (x - 4) (x - 3) (x - 2) (x - 1) x
          (%o3)   -------------------------------------------------
                                        5040
          (%i4) binomial (x + 7, x);
                (x + 1) (x + 2) (x + 3) (x + 4) (x + 5) (x + 6) (x + 7)
          (%o4) -------------------------------------------------------
                                         5040
          (%i5) binomial (11, y);
          (%o5)                    binomial(11, y)

There are also some inexact matches for binomial. Try ?? binomial to see them.

(%o1)                                true
(%i2) 

Binomial Example

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