Summary – Permutation Formula

What is the Permutation Formula?

It is the separate arrangements of a supplied numeral of associates taken one by one, or some, or all at a time. For instance, if we have two elements A and B, there are two possible interpretations, AB and BA....

Permutation Formula Explanation

A permutation is a kind of arrangement that shows how to permute. If there are three separate integers 1, 2, and 3, and if somebody is interested to permute the integers taking 2 at a point, it offers (1, 2), (1, 3), (2, 1), (2, 3), (3, 1), and (3, 2). That is it can be performed in 6 ways. Here, (1, 2) and (2, 1) are separate. Again, if these 3 integers shall be set enduring all at a time, then the arrangements will be (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2) and (3, 2, 1) i.e. in 6 ways. In known, n separate items can be selected accepting r (r < n) at a time in n(n – 1)(n – 2) … (n – r + 1) ways. In particular, the first item can be any of the n items. Now, after selecting the first item, the second item will be any of the remaining n – 1 thing. Similarly, the third item can be any of the remaining n – 2 things. Alike, the rth item can be any of the remaining n – (r – 1) things. Therefore, the total numeral of permutations of n separate items taking r at a time is n(n – 1)(n – 2) … [n – (r – 1)] which is noted as nPr. Or, in other words, nPr = n!/(n – r)!...

Sample Problems on Permutation Formula

Question 1: What are the types of permutations?...

Practice Problems on Permutation Formula

1. There are 4 different colors to paint a car. How many unique color combinations are there if order matters (e.g., red-blue-green is different from green-blue-red)?...

Summary – Permutation Formula

The permutation formula helps you calculate the number of unique arrangements (order matters) for a selection of items from a larger set. It is denoted by nPr, where n is the total number of items and r is the number of items you are choosing to arrange. The formula is nPr = n! / (n – r)!, where n! represents n factorial (n multiplied by all the positive integers less than n)....