PERMUTATION & COMBINATION

Permutation and Combination are both mathematical terms related to each other. Generally, most of the time, students get confused which concept to use in solving the problems. These are precise term and to be used as per the given situation, described in below section examples.

Topics Covered:

What s Permutation?

What is Combination?

Difference between Permutation & Combination.

Formula of Permutation.

Formula of Combination.

Problems on Permutation & Combination.

FAQ’s on Permutation & Combination.

What is Permutation?

Permutation is used to determine the number of possible arrangements where order is Important.

Example of Permutation:

Number Lock:

Suppose we are having a number lock and the password to open the lock is 8967. Here 8, 9, 6 & 7 are four different numbers, and the order of numbers is important to open the lock. This means, the number 8967 in order will open the lock but 8976 will not. Order matters, so it is the case of permutation.

Some other example of Permutation:

(1) In how many ways, we can arrange 4 students in a line?

Note: While arranging students in a line, the order will be important, so it is the case of Permutation

Take Away:

What is Combination?

Combination is used to determine the number of possible arrangements where order is not important.

Example of Combination:

Choose among Kids.

Suppose we are having 3 kids, John, Ana & raj, and we have to choose any of the 2 kids for the Halloween function. Here while choosing 2 kids, the order is not important. It means choosing Ana & John OR John & Ana will be considered the same. Order is not important, so it is the case of the Combination.

Take Away:

Difference Between Permutation & Combination

It is common for many students to get confused in what is the difference between permutation & combination. Permutation & Combination are very related terms but can’t be interchanged. The most important difference between permutation and combination is that in Permutation order is important and in Combination order is not important.

Example of difference between Permutation and Combination

Let’s Understand the difference between Permutation and combination with an example.

Suppose we are having two elements X & Y, and we have to arrange them. If we arrange them keeping order in mind, we can form 2 arrangements. XY and YX. But if we do not keep the order in mind, the arrangement will be just XY. The first case is Permutation, as the order is important, while the Second case is combination, as the order is not important. Refer to the below animation for further understanding.