HYPGEOM.DIST Function
Basic Description
The Excel Hypgeom.Dist function returns the value of the hypergeometric distribution for a specified number of successes from a population sample. The user can specify whether the cumulative distribution or the probability density function should be used.
The function is new in Excel 2010, and so is not available in earlier versions of Excel. However, the probability density hypergeometric distribution can be calculated by the Hypgeomdist function, which is available in earlier versions of Excel.
Syntax: HYPGEOM.DIST( sample_s, number_sample, population_s, number_pop, cumulative )
Where the function arguments are:
sample_s  –  The number of successes in the sample  
number_sample  –  The size of the sample  
population_s  –  The number of successes in the population  
number_pop  –  The size of the population  
cumulative  –  A logical argument that specifies the type of distribution to be calculated. This can have the value TRUE or FALSE, meaning:

The first four arguments to the function should all be integers. If these values are supplied as decimals, they are truncated to integers by Excel.
Hypgeom.Dist Function Examples
Example 1: Probability Density Function
Imagine you have a bag, containing 3 red balls and 9 green balls. If you remove 3 balls from the bag, the probability that 0, 1, 2 or 3 of these balls are red can be calculated is given by the hypergeometric distribution.
These probabilities are calculated by the Excel Hypgeom.Dist function, in cells A2A5 of the spreadsheet on the right. The formulas are shown in the upper spreadsheet and the results are shown in the spreadsheet below.
Note that this example calculates the probability density function. This gives the probability of exactly sample_s successes occurring.
Formulas:

Results:

Example 2: Cumulative Distribution Function
Imagine that you have the same bag as in Example 1 (above), which again, contains 3 red balls and 9 green balls.
The Excel Hypgeom.Dist function, can also be used to the calculate the probability of at most 0, 1, 2 or 3 red balls being selected from a sample of 3 balls, taken from the bag. This is shown in the spreadsheet on the right. Again, the formulas are shown in the upper spreadsheet and the results are shown in the lower spreadsheet.
Formulas:

Results:

Hypgeom.Dist Function Errors
If you get an error from the Excel Hypgeom.Dist function this is likely to be one of the following :
#NUM!  –  Occurs if either:


#VALUE!  –  Occurs if any of the supplied arguments are not recognised as numeric values 