## Combination Calculator “Fun Way to Calculate Combinations”

A combination calculator is the most simplest tool to solve combination problems. What is really important to use a combination calculator is to understand the basic formula and functionality of the calculator. We are in a very competitive world. You can find yourself to cope with this competition as there are many online available combinations calculators. But the main problem with such type of calculators is either they are not user-friendly or they or not free to use. Here our combination calculator surpasses every other online accessible calculator on account of its easy to use nature and simple to utilize (UI).

## What are Permutations and Combinations?

To understand what a combination is, we need to understand a permutation first. Both the permutations and combinations are the branch of mathematics known as combinatorics. In this branch of mathematics, we study finite, discrete structures. A permutation is a unique way of several objects that could be ordered or chosen.

For instance, on the off chance that we had three letters ABC, we could arrange them as ABC or BCA. These would be two different permutations. A third permutation would be CAB. What we need to know is how many permutations of these objects are there. As you have seen, the number of alphabets entered is substantial; ABC is not the same as BCA. Whereas in combinations, any order of those three alphabets would suffice.

## Combinations “A Brief Overview of Combinations”

Numbers of different groups that can be formed by selecting some or all the items are called combinations of those numbers. Whereas, the numbers of different arrangements that can be made by taking some or all of those items called permutations. So while calculating any of combinations or permutations, keep the difference in mind to find the right answer.

## How to Calculate Combinations and Permutations?

When these are "n" things and we make courses of action of them taking "r" at a time we get ^{n}P_{r} plans. Where ^{n}P_{r} defines several "n” things taken “r” at a time.

## Combination Formula

The formula of Combination is _{n}P^{r} means the number of Combination without repetition of "n" things take "r" at a time.

^{n}C_{r} = n! / r! (n-r)!

## Solved Examples of Combination

### Example 1:

Find how many ways a cricket team having 11 players can be formed from 15 high-class payers available?

Solution: As per combination definition and formula, the value of “n” (total players) is 15 and the value of “r” (players to be chosen) is 11.

By putting the estimations of both "n" and "r" in the Combination's equation we get

^{15}C_{11} = 1365

So, a team can be formed in 1365 ways

### Example 2:

A committee of 5 people is to be chosen from 6 men and 4 women. How many committees are possible if

**a) **There are no restrictions?

**Sol:** ^{10}C_{5}

**b) **One specific individual must be picked on the advisory group?

**Sol:** 1 x ^{9}C_{4}

**c) **One specific lady must be prohibited from the advisory group?

**Sol:** ^{9}C_{5}

### Example 3:

In a hand of poker, 5 cards are managed from an ordinary pack of 52 cards.

(i) What is the all-out conceivable number of hands if there are no limitations?

**Sol:** ^{52}C_{5}

**a)** In what number of these hands are there

**b)** 4 Kings?

**Solution:** ^{4}C_{4} x ^{48}C_{1} or 1 x 48

### Example 4:

If 4 Math books are selected from 6 different math books and 3 English books are chosen from 5 different English books, how many ways can the seven books be arranged on a shelf?

**a)** If there are no restrictions?

**Sol:** ^{6}C_{4} x ^{5}C_{3} x 7!

**b)** If the g math’s books remain together?

**Sol:**

This one can be explained with both Permutation and Combination. So, the answer is

^{6}P_{4} x ^{5}C_{3} x 4! Or (^{6}C_{4} x 4!) x ^{5}C_{3} x 4!

## How does one can identify if a given problem is a permutation or Combination?

Permutation and Combination are utilized to discover from various perspectives we can get a specific number of articles from a given number of items in a gathering. At the point when it is an issue of just getting or picking the things, it is an issue of Combination. It resembles choosing a group of state 11 players out of accessible, state, 100 players. For this circumstance, when you circulate a once-over, it isn't noteworthy who was picked first.

In Permutation the order is essential. In the above case suppose you take a photograph of 11 players, then even by changing the position of one player we will get a different photo. Each different position is a separate order or arrangement. So in Permutation, there is Selection and arrangement whereas in Combination there is the only selection.

## Formula of Permutation:

^{n}P_{r} = n (n-1) (n-2) (n-3) …………. (n-r+1) = n! / (n-r)!

Key things to remember while calculating Permutation

- Permutation where a particular item is to be in the specified place
- Roundabout Permutation when there are "n" objects they can be organized in (n-1) ways
- Permutations of things not all different n! / p! q! r!
- Permutation with repetition n
^{r}

## How to use a Combination Calculator?

Our Combination calculator is a tool that helps you not only determine the number of combinations, but it also shows the possible sets you can make with every single Combination. This calculator is purely working on nCr to get you the most trustable and exact results without taking much of your time. If you want to know how many combinations can be made out of a particular number, try our combination calculator. To use our combination calculator, you need to perform the following steps

- Enter the estimation of "n" in the first field
- Enter the estimation of “r” in the second field
- Click on the “CALCULATE” button

After clicking on the calculate button, you will get the combinations of a specific number within a few seconds.