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Choose Calculator + Online Solver With Free Steps
The online Choose Calculator is a free tool that helps to solve all kinds of combination expressions swiftly. The combination means choosing elements from a group irrespective of their selection order.
The calculator takes the total number and the number of elements you want to choose as input and calculates the combinations that represent the number of ways you can choose the elements.
What Is a Choose Calculator?
A Choose Calculator is an online calculator specifically designed to quickly solve combination-related problems.
Combinations are widely used in real-life scenarios where we want to pick certain objects out of a bigger list. For instance, selecting nominees for council or choosing items from a menu, etc.
That’s why researchers in the fields like communication, maths, and finance frequently use them in their work. The number of possible combinations is calculated by a specific formula that uses factorial.
To fastly calculate the results of the combinations in the problems you can use Choose Calculator. It solves the combination in less than a second no matter how bigger is the expression.
It is the most reliable tool as it gives a state-of-the-art performance. This calculator works in your browser without any installation process. The interface is simple and anyone can operate the tool without any hassle.
How To Use the Choose Calculator?
You can use the Choose Calculator by inserting several combinations in the given boxes. You just need to enter them and click the button to get your desired results in front of you.
Following are the simple steps on how to use the calculator. You must follow them to get the correct results.
Step 1
Enter the total number of items in the box with the label “N.”
Step 2
Then put the number of items you want to select from the total items in the R box. It must be less than the N.
Step 3
Press the Solve button for further processing. It will display the numerical value obtained as a result of solving the combination.
How Does the Choose Calculator Work?
The Choose calculator works by finding the number of possible combinations by selecting some number of elements from a given larger set. This calculator determines the number of possible subsets that can be made from the larger set.
The concept of combinations has great importance in the field of mathematics and statistics, therefore we should know the concept of combinations to use this calculator properly.
Combination
Combinations are the selections that are made by choosing a few or every number of objects from a given set of objects irrespective of their arrangements. The combinations focus on the selection of items rather to arrange them.
The combinations of different objects can be found by the combinations formula which is represented in the following way:
\[ ^{n}C_{r} = \frac{n!}{(n-r)!r!} \]
Where n is the total number of elements in the set, r is the number of elements to be chosen out of n elements, and n, r is always a positive integer. The number of elements to be chosen is always less than or equal to the total number of elements.
The above formula needs to find the factorial of a number. A factorial of any number is calculated by taking the product of all positive integers which is less than or equal to that number.
The combinations are obtained by the combination formula, applying factorials, and in terms of permutation. This calculator also applies the above formula to calculate the combinations.
Suppose there is a set of n elements and there is a requirement for finding the combinations in which r elements can be selected out of the set of $n$ elements.
This can be found by first finding the number of all permutations of n elements taken r at a time given by $^{n}P_{r}$. Then each combination will be counted r! times in the obtained permutations.
Hence, the total number of permutations and combinations of n elements, taken r at a time is obtained by applying the $^{n}C_{r}$ formula.
There are two types of combinations since the arrangement of the elements does not matter. One type is combinations with the repetition of things and the other type is combinations without the repetition.
Difference Between Combination and Permutation
The difference between combinations and permutations should be clear to apply the correct usage of their formulae in different situations.
Permutations are used when there is a requirement to arrange things in a specific sequence or order whereas combinations are needed to find the number of possible groups of the things irrespective of their order.
Permutations are applied to things of a different type while on the contrary the combinations are used for things of the same type.
When the permutations are to be found, the different possible sorting is counted whereas the combinations require the counting of only different possible subgroups that’s why the value of the combination is always less than the value of the permutation.
The combination and permutations can be found in a single formula. The permutation of $n$ things taken ‘r’ at a time is equivalent to the product of r factorial and combination.
\[ ^{n}P_{r}= r! *\, ^{n}C_{r} \]
Solved Examples
Here are some solved problems by the calculator.
Example 1
An athletics coach needs to select three runners among the seven available athletes. Use the Choose calculator to find out in how many ways selection can be done.
Solution
The solution to the problem is given below. The total number of athletes is seven so N = 7 and the coach needs to select three therefore R=3.
\[ ^{7}C_{3} = \frac{7!}{(7-3)!\cdot3!} = \frac{7!}{4!\cdot3!} = 35 \]
There is a total of 35 ways in which the coach can perform selections.
Example 2
A university student is selected for a bachelor’s program. He can only pick 4 courses out of 8 listed courses in his first semester. How many ways are possible to select these four courses?
Solution
The total courses in the list are eight so N = 14 and the student can choose four courses therefore R = 5.
\[ ^{8}C_{4} = \frac{8!}{(8-4)!\cdot4!} = \frac{8!}{4!\cdot4!} = 70 \]
There is a total of 70 combinations of selecting subjects for the student.