Permutations calculator12/12/2023 This cookie is set by GDPR Cookie Consent plugin. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookie is used to store the user consent for the cookies in the category "Analytics". These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. This online calculator uses arbitrary-precision decimal arithmetic, so that you can get the exact value of the number of permutations even for a sufficiently large value of \(n\) within a reasonable time span (depending on the computational power of you computer). Using our Permutations Calculator it’s easy to find \(P(15,3)\) = 2730 possible outcomes. So, we have to calculate \(P(15,3)\) in order to find the total number of possible outcomes for the top 3 runners. How many different permutations are there for the top 3 from the 15 contestants?įor this problem we are looking for an ordered subset of 3 contestants (\(k\)) from the 15 contestants (\(n\)) taking place in the competition. The runner, finished first, receives the gold medal, the runner, finished second, receives the silver medal and the runner, finished third, receives the bronze medal. $$įor example, lets consider a running competition with 15 contestants. The number of permutations \(P(n,k)\) is defined as the number of ways of obtaining an ordered subset of \(k\) elements from a set of \(n\) elements and given by the formula:
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