MULTINOMIAL

The function MULTINOMIAL takes a List of Numbers in the form ([n_1, n_2, n_3,...n_m]) and returns ({(\Sigma{i=1}^m n_i)! \over \Pi{i=1}^m (n_i!)}).

This function takes a List of Numbers as input. It returns another Number: the factorial of the sum of every Number in the given List divided by the product of the factorial of every Number in the given List.

Declaration

MULTINOMIAL(list_of_numbers) -> number

Parameters

list_of_numbers (required, type: List)
A List of Numbers. There is no upper limit to the number of items that can occupy this List.

Return Values

number (required, type: Number)
The factorial of the sum of every Number in the given List divided by the product of the factorial of every number in the given List.
If the List of Numbers is in the form ([n_1, n_2, n_3,...n_m]), then number can be written as: $$ {(\Sigma{i=1}^m n_i)! \over \Pi{i=1}^m (n_i!)}.$$

Examples

The following example takes the List [1, 2, 3] and returns ({(1 + 2 + 3)! \over 1!2!3!} ):

MULTINOMIAL([1, 2, 3]) -> 60