If the order doesn't matter then we have a combination, if the order does matter then we have a permutation. One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: **P(n,r)=n!**

This was British mathematician **Arthur Cayley** (1821-1895), the first to write down something that looks like our modern definition of a "group"1. wob aida of mathematics. The symmetric groups Sn (recall that Sn is the group of permutations of n objects) are particularly important.

**nCr is the number of selecting r things out of n things**. Whenever we select r things, we reject n-r things. So the number of ways of rejecting n - r things (which is nCn-r) is same as the number of ways of selecting r things out of n things (which is nCr). Therefore, nCn-r = nCr.

A permutation is **a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters**.

**nCr is the number of selecting r things out of n things**. Whenever we select r things, we reject n-r things. So the number of ways of rejecting n - r things (which is nCn-r) is same as the number of ways of selecting r things out of n things (which is nCr). Therefore, nCn-r = nCr.

To calculate permutations, we use the equation nPr, where n is the total number of choices and r is the amount of items being selected. To solve this equation, use the equation **nPr = n! / (n - r)!**.

**It's easy, too damn easy**. Just think of anything you can and imagine the number of ways to arrange, derange, permute or divide that thing (if possible). You can create an infinite number of questions. One needs to be that curious to actually come out as a winner and conqueror of this topic.

Once you are thorough with the trips to solve the problems on permutation and combination, the topics will be pretty much more comfortable in maths. One thing can be said about these topics is that **these two are easy when compared with other topics**, for example, topics of calculus.

In probability, nCr **states the selection of 'r' elements from a group or set of 'n' elements, such that the order of elements does not matter**. The formula to find combinations of elements is: nCr = n!/

Permutation: **nPr represents the probability of selecting an ordered set of 'r' objects from a group of 'n' number of objects**. The order of objects matters in case of permutation. The formula to find nPr is given by: nPr = n!/(n-r)!

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula **nCr = n! / r!** *** (n - r)!**, where n represents the total number of items, and r represents the number of items being chosen at a time.

A permutation is **an arrangement of objects, without repetition, and order being important**. Another definition of permutation is the number of such arrangements that are possible. Since a permutation is the number of ways you can arrange objects, it will always be a whole number.

The value of factorial of 10 is 3628800, i.e. **10!** **= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1** = 3628800.

**Permutations are for lists (where order matters) and combinations are for groups (where order doesn't matter)**. In other words: A permutation is an ordered combination. Note: A “combination” lock should really be called a “permutation” lock because the order that you put the numbers in matters.

Combinations can be confused with permutations. However, **in permutations, the order of the selected items is essential**. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.

In both permutations and combinations, **repetition is not allowed**.

**nCr = n!/** Where n is the total number of objects and r is the number of selected objects.

Remember that combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula **nCr = n! / r!** *** (n - r)!**, where n represents the number of items, and r represents the number of items being chosen at a time.

**Combinations are much easier to get along with – details don't matter so much**. To a combination, red/yellow/green looks the same as green/yellow/red. Permutations are for lists (where order matters) and combinations are for groups (where order doesn't matter). In other words: A permutation is an ordered combination.

If the order doesn't matter then we have a combination, if the order does matter then we have a permutation. One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: **P(n,r)=n!**

Given an array arr containing N positive integers, the task is to check if the given array arr represents a permutation or not. **A sequence of N integers is called a permutation if it contains all integers from 1 to N exactly once**. Examples: Input: arr[] = {1, 2, 5, 3, 2}

Dated : 06-Jun-2022

Category : Education