# HYPGEOMDIST

Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of sample successes, given the sample size, population successes, and population size. Use HYPGEOMDIST 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**

**HYPGEOMDIST**(**sample_s**,**number_sample**,**population_s**,**number_population**)

**Sample_s** is the number of successes in the sample.

**Number_sample** is the size of the sample.

**Population_s** is the number of successes in the population.

**Number_population** is the population size.

**Remarks**

- All arguments are truncated to integers.
- If any argument is nonnumeric, HYPGEOMDIST returns the #VALUE! error value.
- If sample_s < 0 or sample_s is greater than the lesser of number_sample or population_s, HYPGEOMDIST returns the #NUM! error value.
- If sample_s is less than the larger of 0 or (number_sample - number_population + population_s), HYPGEOMDIST returns the #NUM! error value.
- If number_sample < 0 or number_sample > number_population, HYPGEOMDIST returns the #NUM! error value.
- If population_s < 0 or population_s > number_population, HYPGEOMDIST returns the #NUM! error value.
- If number_population < 0, HYPGEOMDIST returns the #NUM! error value.
- The equation for the hypergeometric distribution is:
where:

x = sample_s

n = number_sample

M = population_s

N = number_population

HYPGEOMDIST 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:

`HYPGEOMDIST(1,4,8,20)`

equals 0.363261