The MULTINOMIAL function returns the ratio of the factorial of a sum of values to the product of factorials.  The multinomial is:  

    \[    MULTINOMIAL(a_1,a_2, \dots, a_n) = \frac {(a_1 + a_2 + \dots + a_n)!}{a_1! a_2! \dots a_n!}   \]

Syntax

=MULTINOMIAL(num_1,[num_2], … )

Note: Beginning with Excel 2007, you can supply up to 255 values to the function. Excel 2003 would only accept up to 29 number arguments.

Arguments

Argument Description
num_1,
[num_2], …
num_1 is required, subsequent numbers are optional. 1 to 255 values for which you want the multinomial

Examples

  A B C
1 Formula Result Notes
2 =MULTINOMIAL(2,3,4) 1,260 Ratio of the factorial of the sum of 2,3, and 4 (362880) to the product of the factorials of 2,3, and 4 (288)
3 =MULTINOMIAL(3,1,2,5) 27,720 Ratio of the factorial of the sum of 3,1,2, and 5 to the product of the factorials of 3,1,2, and 5

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if any of the supplied arguments are non-numeric
#NUM! Occurs if any of the supplied arguments are less than 0
#NAME? Occurs when Analysis ToolPak add-in is not enabled