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? multinomial;

Calculate

##### multinomial-permutations

permutations ([1,4,5,...

multinomial(11, [1,4...

Calculate

? multinomial;

Calculate

##### multinomial-permutations

permutations ([1,4,5,...

multinomial(11, [1,4...

Calculate

### multinomial

Run Example
```(%i1)load(functs);
(%o1)      /usr/share/maxima/5.21.1/share/simplification/functs.mac
(%i2) multinomial(11, [4, 2, 2, 1]);
resolvante
generale

NOTE: To compile the system do
load("sym/compile");
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
(%o2)                               207900
(%i3) multinomial_coeff(4, 2, 2, 1);
(%o3)                                3780
(%i4) ```
Run Example
```load(functs);
(%o1)      /usr/share/maxima/5.21.1/share/simplification/functs.mac
(%i2) 11!/(4!*4!*2!*1!);
(%o2)                                34650
(%i3) multinomial(11, [4, 4, 2, 1]);
resolvante
generale

NOTE: To compile the system do
load("sym/compile");
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
(%o3)                                34650
(%i4) multinomial_coeff(4, 4, 2, 1);
(%o4)                                34650
(%i5) permutation(4, 2);
(%o5)                                 12
(%i6) permutations([t, o, o, l]);
(%o6) {[l, o, o, t], [l, o, t, o], [l, t, o, o], [o, l, o, t], [o, l, t, o],
[o, o, l, t], [o, o, t, l], [o, t, l, o], [o, t, o, l], [t, l, o, o],
[t, o, l, o], [t, o, o, l]}
(%i7) length(permutations([t, o, o, l]));
(%o7)                                 12
(%i8) combination(4, 2);
(%o8)                                  6
(%i9) ```
Run Example
```permutations ([1,4,5,7,0]);
(%o1) {[0, 1, 4, 5, 7], [0, 1, 4, 7, 5], [0, 1, 5, 4, 7], [0, 1, 5, 7, 4],
[0, 1, 7, 4, 5], [0, 1, 7, 5, 4], [0, 4, 1, 5, 7], [0, 4, 1, 7, 5],
[0, 4, 5, 1, 7], [0, 4, 5, 7, 1], [0, 4, 7, 1, 5], [0, 4, 7, 5, 1],
[0, 5, 1, 4, 7], [0, 5, 1, 7, 4], [0, 5, 4, 1, 7], [0, 5, 4, 7, 1],
[0, 5, 7, 1, 4], [0, 5, 7, 4, 1], [0, 7, 1, 4, 5], [0, 7, 1, 5, 4],
[0, 7, 4, 1, 5], [0, 7, 4, 5, 1], [0, 7, 5, 1, 4], [0, 7, 5, 4, 1],
[1, 0, 4, 5, 7], [1, 0, 4, 7, 5], [1, 0, 5, 4, 7], [1, 0, 5, 7, 4],
[1, 0, 7, 4, 5], [1, 0, 7, 5, 4], [1, 4, 0, 5, 7], [1, 4, 0, 7, 5],
[1, 4, 5, 0, 7], [1, 4, 5, 7, 0], [1, 4, 7, 0, 5], [1, 4, 7, 5, 0],
[1, 5, 0, 4, 7], [1, 5, 0, 7, 4], [1, 5, 4, 0, 7], [1, 5, 4, 7, 0],
[1, 5, 7, 0, 4], [1, 5, 7, 4, 0], [1, 7, 0, 4, 5], [1, 7, 0, 5, 4],
[1, 7, 4, 0, 5], [1, 7, 4, 5, 0], [1, 7, 5, 0, 4], [1, 7, 5, 4, 0],
[4, 0, 1, 5, 7], [4, 0, 1, 7, 5], [4, 0, 5, 1, 7], [4, 0, 5, 7, 1],
[4, 0, 7, 1, 5], [4, 0, 7, 5, 1], [4, 1, 0, 5, 7], [4, 1, 0, 7, 5],
[4, 1, 5, 0, 7], [4, 1, 5, 7, 0], [4, 1, 7, 0, 5], [4, 1, 7, 5, 0],
[4, 5, 0, 1, 7], [4, 5, 0, 7, 1], [4, 5, 1, 0, 7], [4, 5, 1, 7, 0],
[4, 5, 7, 0, 1], [4, 5, 7, 1, 0], [4, 7, 0, 1, 5], [4, 7, 0, 5, 1],
[4, 7, 1, 0, 5], [4, 7, 1, 5, 0], [4, 7, 5, 0, 1], [4, 7, 5, 1, 0],
[5, 0, 1, 4, 7], [5, 0, 1, 7, 4], [5, 0, 4, 1, 7], [5, 0, 4, 7, 1],
[5, 0, 7, 1, 4], [5, 0, 7, 4, 1], [5, 1, 0, 4, 7], [5, 1, 0, 7, 4],
[5, 1, 4, 0, 7], [5, 1, 4, 7, 0], [5, 1, 7, 0, 4], [5, 1, 7, 4, 0],
[5, 4, 0, 1, 7], [5, 4, 0, 7, 1], [5, 4, 1, 0, 7], [5, 4, 1, 7, 0],
[5, 4, 7, 0, 1], [5, 4, 7, 1, 0], [5, 7, 0, 1, 4], [5, 7, 0, 4, 1],
[5, 7, 1, 0, 4], [5, 7, 1, 4, 0], [5, 7, 4, 0, 1], [5, 7, 4, 1, 0],
[7, 0, 1, 4, 5], [7, 0, 1, 5, 4], [7, 0, 4, 1, 5], [7, 0, 4, 5, 1],
[7, 0, 5, 1, 4], [7, 0, 5, 4, 1], [7, 1, 0, 4, 5], [7, 1, 0, 5, 4],
[7, 1, 4, 0, 5], [7, 1, 4, 5, 0], [7, 1, 5, 0, 4], [7, 1, 5, 4, 0],
[7, 4, 0, 1, 5], [7, 4, 0, 5, 1], [7, 4, 1, 0, 5], [7, 4, 1, 5, 0],
[7, 4, 5, 0, 1], [7, 4, 5, 1, 0], [7, 5, 0, 1, 4], [7, 5, 0, 4, 1],
[7, 5, 1, 0, 4], [7, 5, 1, 4, 0], [7, 5, 4, 0, 1], [7, 5, 4, 1, 0]}
(%i2)  multinomial(11, [1,4,5,7,0]);
resolvante
generale

NOTE: To compile the system do
load("sym/compile");
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
(%o2)                                  0
(%i3) ```

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