How to Calculate Combination Probability?

Combination is a mathematical concept which helps us in determining the possible outcomes of an event. To calculate combination probability we have to follow several steps and utilize several formulas. They are discussed below:

Understand the Mathematical Notation of Combination

In combination probability, different formulas are required to solve various problems. But the basic concept behind those formulas are same. To calculate combination probability, we use several terms and notations, which are:

• Factorial notation: Factorial notation is a exclamatory mark right to the next of a number. It is a mathematical symbol. For example: 3! is equivalent to 3 × 2 × 1.
• Pascal’s triangle: We can find solutions of several combination probability problems by using Pascal’s triangle concept.
• Variable “n” : variable n represents the total number of outcomes of an event. For example, A lock with 3 digits, each of which can be 0 to 9, has an n value of 10 because there are 10 possible digits for each spot in combination.
• Variable “r” : variable r is used to identify the possible items of an event.

Identify the Style of Calculation

In order to apply correct formula for calculating problems on combination, it is important to understand the type of calculation you are performing. The first thing to notice is whether the calculation is a permutation or combination. Then you must note that is there any repetition of the same value during the combination. At the end there will be four calculation types, one pair consisting repeat and no repeat of combination and another for permutation.

Choose the Appropriate Formula

After identifying the correct style of the calculation, it is important to use the correct formula to find the probability of a specific outcome. The four combination probability equations are:

• Permutation with repetition , total permutation = n^r
• Permutation without repetition, total permutation = n!/(n-r)!
• Combination without repetition , total combination = n!/(n-r)!r!
• Combination with repetition , total combination = (r+n-1)!/r!(n-1)!

Input variables and Calculate the Probability

After selecting appropriate formula, now put all the values to calculate the combination. The probability for each combination can be calculated by dividing the number of favorable combinations by total number of combinations. Then combining the number of favorable combinations with the individual probabilities, we get overall combination probability.

Also, Check

• Baye’s Theorem
• Probability Distribution
• Conditional Probability

Combination probability is a mathematical method that involves the process of combination in determining the number of favorable outcomes of an event. We use combinations in probability problems to determine a sequence of outcomes where the order of the outcomes does not matter. Understanding how to calculate combination probability can be a useful mathematical skill in the field of math and science.

In this article, we will discuss in detail the definitions of combination and probability and how to calculate combination probability with solved examples.