Combination Probability Calculator

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✖N Set is the total number of the available sets from which items will be selected.ⓘ N Set [n]			+10% -10%
✖R Items are the total items that can be selected from the available set.ⓘ R Items [r]			+10% -10%

✖Combination Probability is the number of ways of selecting r items from a set of n.ⓘ Combination Probability [nCr]

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Credits

Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has created this Calculator and 500+ more calculators!

Himanshi Sharma

Bhilai Institute of Technology (BIT), Raipur

Himanshi Sharma has verified this Calculator and 500+ more calculators!

Combination Probability Solution

STEP 0: Pre-Calculation Summary

Formula Used

combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!)
nCr = (n)!/((r)!*(n-r)!)
This formula uses 2 Variables

Variables Used

N Set- N Set is the total number of the available sets from which items will be selected.
R Items- R Items are the total items that can be selected from the available set.

STEP 1: Convert Input(s) to Base Unit

N Set: 20 --> No Conversion Required
R Items: 9 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

nCr = (n)!/((r)!*(n-r)!) --> (20)!/((9)!*(20-9)!)

Evaluating ... ...

nCr = 167960

STEP 3: Convert Result to Output's Unit

167960 --> No Conversion Required

FINAL ANSWER

167960 <-- Combination Probability (nCr)

(Calculation completed in 00.000 seconds)

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< 6 Probability Calculators

Binomial Probability

binomial_probability = Combination Probability (nCr)*((Probability of Success)^R Items)*((Probability of Failure)^(N Set-R Items)) Go

Combination Probability

combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!) Go

Empirical Probability

empirical_probability = Number of times event occurs/Total number of times experiment performed Go

Probability of event

probability_of_an_event = Number of Favorable Outcomes/Total Number of Possible Outcomes Go

Probability of failure

probability_of_failure = 1-Probability of Success Go

Probability of success

probability_of_success = 1-Probability of Failure Go

Combination Probability Formula

combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!)
nCr = (n)!/((r)!*(n-r)!)

What is Combination Probability?

Combination Probability is the number of ways of selecting r items from a set of n. A combination is an unordered collection of unique elements. Given the set, n, of all possible unique elements, a combination is a subset of the elements of n. The order of the elements in a combination is not important. Additionally, the elements cannot be repeated in a combination (i.e., every element appears once); this is often referred to as "without replacement/repetition".

How to Calculate Combination Probability?

Combination Probability calculator uses combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!) to calculate the Combination Probability (nCr), Combination Probability is the number of ways of selecting r items from a set of n. Combination Probability (nCr) and is denoted by nCr symbol.

How to calculate Combination Probability using this online calculator? To use this online calculator for Combination Probability, enter N Set (n) & R Items (r) and hit the calculate button. Here is how the Combination Probability calculation can be explained with given input values -> 167960 = (20)!/((9)!*(20-9)!) .

FAQ

What is Combination Probability?

Combination Probability is the number of ways of selecting r items from a set of n and is represented as nCr = (n)!/((r)!*(n-r)!) or combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!) . N Set is the total number of the available sets from which items will be selected & R Items are the total items that can be selected from the available set.

How to calculate Combination Probability?

Combination Probability is the number of ways of selecting r items from a set of n is calculated using combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!) . To calculate Combination Probability, you need N Set (n) & R Items (r). With our tool, you need to enter the respective value for N Set & R Items and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Combination Probability (nCr)?

In this formula, Combination Probability (nCr) uses N Set & R Items. We can use 6 other way(s) to calculate the same, which is/are as follows -

probability_of_an_event = Number of Favorable Outcomes/Total Number of Possible Outcomes
combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!)
binomial_probability = Combination Probability (nCr)*((Probability of Success)^R Items)*((Probability of Failure)^(N Set-R Items))
empirical_probability = Number of times event occurs/Total number of times experiment performed
probability_of_failure = 1-Probability of Success
probability_of_success = 1-Probability of Failure

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