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The Maxima on-line user's manual

Algebra Calculator

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Multinomial_coeff Calculator

Multinomial_coeff

Function: multinomial_coeff (<a_1>, ..., <a_n>)

load(functs);
length(permutations([m, i, s, s, i, s, i, p, i]));
multinomial_coeff(4, 3, 1, 1);
multinomial(9,[4, 3, 1, 1]);
11!/(4!*4!*2!*1!);
multinomial(11, [4, 4, 2, 1]);
multinomial_coeff(4, 4, 2, 1);
permutations([t, o, o, l]);
length(permutations([t, o, o, l]));
permutation(4, 2);
multinomial(4, [1, 2, 1]);
multinomial_coeff(1, 2, 1);
plot2d( [discrete, [[1, 1], [1, 2], [1, 3] ]]);
plot2d( [discrete, [[1, 1], [2, 1], [3, 1] ]]);

Function: multinomial_coeff () Returns the multinomial coefficient.

When each <a_k> is a nonnegative integer, the multinomial coefficient gives the number of ways of placing <a_1> + ... + <a_n> distinct objects into n boxes with <a_k> elements in the kth box. In general, multinomial_coeff (<a_1>, ..., <a_n>) evaluates to (<a_1> + ... + <a_n>)!/(<a_1>! ... <a_n>!).

multinomial_coeff() (with no arguments) evaluates to 1.

minfactorial may be able to simplify the value returned by multinomial_coeff.

Examples:

          (%i1) multinomial_coeff (1, 2, x);
                                      (x + 3)!
          (%o1)                       --------
                                        2 x!
          (%i2) minfactorial (%);
                               (x + 1) (x + 2) (x + 3)
          (%o2)                -----------------------
                                          2
          (%i3) multinomial_coeff (-6, 2);
                                       (- 4)!
          (%o3)                       --------
                                      2 (- 6)!
          (%i4) minfactorial (%);
          (%o4)                          10

(%o1)                                true
(%i2) 

Multinomial_coeff Example

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