### The Maxima on-line user's manual

Algebra Calculator

#### Multinomial_coeff

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

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) ```

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