HYPGEOM.DIST function
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
A sampler of chocolates contains 20 pieces. Eight pieces are caramels, and the remaining 12 are nuts. If a person selects 4 pieces at random, the following function returns the probability that exactly 1 piece is a caramel.
The example may be easier to understand if you copy it to a blank worksheet.
How do I copy an example?

Select the example in this article.
Important Do not select the row or column headers.
Selecting an example from Help

Press CTRL+C.

In Excel, create a blank workbook or worksheet.

In the worksheet, select cell A1, and press CTRL+V.
Important For the example to work properly, you must paste it into cell A1 of the worksheet.

To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.
After you copy the example to a blank worksheet, you can adapt it to suit your needs.

