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Multinomial

MULTINOMIAL Function

The MULTINOMIAL function in Excel returns the ratio of the factorial of the sum of values to the product of the factorials of the values. It is used to calculate multinomial coefficients, which are useful in combinatorics and statistics.

Syntax:

MULTINOMIAL(number1, [number2], ...)
  • number1, number2, ...: Numbers or values for which you want to calculate the multinomial. You can input up to 255 values.

Examples:

  1. Basic Multinomial Calculation
    Formula: =MULTINOMIAL(2, 3, 4)
    Returns: 1260
    Explanation: Multinomial is calculated as (2+3+4)! / (2! * 3! * 4!) = 1260.

  2. Multinomial with Equal Values
    Formula: =MULTINOMIAL(3, 3, 3)
    Returns: 1680
    Explanation: (3+3+3)! / (3! * 3! * 3!) = 1680.

  3. Multinomial with Zeros
    Formula: =MULTINOMIAL(4, 0, 2)
    Returns: 15
    Explanation: (4+0+2)! / (4! * 0! * 2!) = 15.

Usage Notes:

  • All input values must be non-negative integers; otherwise, Excel will return a #NUM! error.
  • If any argument is non-numeric, MULTINOMIAL will return a #VALUE! error.
  • The MULTINOMIAL function is particularly useful for multinomial expansions and combinatorial calculations in probability and statistics.