HYPGEOM.DIST function
This article describes the formula syntax and usage of the HYPGEOM.DIST function in Microsoft Excel.
Returns the hypergeometric distribution. HYPGEOM.DIST returns the probability of a given number of sample successes, given the sample size, population successes, and population size. Use HYPGEOM.DIST for problems with a finite population, where each observation is either a success or a failure, and where each subset of a given size is chosen with equal likelihood.
Syntax
HYPGEOM.DIST(sample_s,number_sample,population_s,number_pop,cumulative)
The HYPGEOM.DIST function syntax has the following arguments:

Sample_s Required. The number of successes in the sample.

Number_sample Required. The size of the sample.

Population_s Required. The number of successes in the population.

Number_pop Required. The population size.

Cumulative Required. A logical value that determines the form of the function. If cumulative is TRUE, then HYPGEOM.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.
Remarks

All arguments are truncated to integers.

If any argument is nonnumeric, HYPGEOM.DIST returns the #VALUE! error value.

If sample_s < 0 or sample_s is greater than the lesser of number_sample or population_s, HYPGEOM.DIST returns the #NUM! error value.

If sample_s is less than the larger of 0 or (number_sample  number_population + population_s), HYPGEOM.DIST returns the #NUM! error value.

If number_sample ≤ 0 or number_sample > number_population, HYPGEOM.DIST returns the #NUM! error value.

If population_s ≤ 0 or population_s > number_population, HYPGEOM.DIST returns the #NUM! error value.

If number_pop ≤ 0, HYPGEOM.DIST returns the #NUM! error value.

The equation for the hypergeometric distribution is:
where:
x = sample_s
n = number_sample
M = population_s
N = number_pop
HYPGEOM.DIST is used in sampling without replacement from a finite population.
Example
Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.
Data 
Description 
Result 
1 
Number of successes in the sample 

4 
Sample size 

8 
Number of successes in the population 

20 
Population size 

Formula 
Description (Result) 

=HYPGEOM.DIST(A2,A3,A4,A5,TRUE) 
Cumulative hypergeometric distribution function, for sample and population in cells A2 through A5. 
0.4654 
=HYPGEOM.DIST(A2,A3,A4,A5,FALSE) 
Probability hypergeometric distribution function, for sample and in cells A2 through A5. 
0.3633 