Last updated on August 5th, 2025
A calculator is a tool designed to perform both basic arithmetic operations and advanced calculations, such as those involving trigonometry. It is especially helpful for completing mathematical school projects or exploring complex mathematical concepts. In this topic, we will discuss the Permutation And Combination Calculator.
The Permutation And Combination Calculator is a tool designed for calculating permutations and combinations.
Permutations are arrangements where the order matters, while combinations are selections where the order does not matter.
These concepts are vital in fields like statistics, probability, and various branches of mathematics.
The terms permutation and combination come from Latin: permutationem (meaning "interchange") and combinare (meaning "to join together").
For calculating permutations and combinations using the calculator, follow the steps below -
Step 1: Input: Enter the total number of items (n) and the number of items to pick (r).
Step 2: Choose: Select whether you want to calculate permutations or combinations.
Step 3: Click: Calculate. By doing so, the numbers you have given as input will be processed.
Step 4: You will see the result in the output column.
Mentioned below are some tips to help you get the right answer using the Permutation And Combination Calculator.
Know the formulas: The formula for permutations is P(n,r) = n! / (n-r)!, and for combinations, it is C(n,r) = n! / [r! (n-r)!], where ‘n’ is the total number of items, and ‘r’ is the number of items to pick.
Use the Right Units: When dealing with permutations and combinations, ensure you're considering the correct number of items and selections.
Enter correct Numbers: When entering the values for ‘n’ and ‘r’, make sure the numbers are accurate.
Small mistakes can lead to incorrect results, especially with larger numbers.
Calculators mostly help us with quick solutions.
For calculating complex math questions, students must know the intricate features of a calculator.
Given below are some common mistakes and solutions to tackle these mistakes.
Help Sarah find how many different ways she can arrange 5 books on a shelf.
There are 120 different ways to arrange the 5 books.
To find the number of arrangements, we use the permutation formula: P(n,r) = n! / (n-r)! Here, n=5 and r=5 (since she is arranging all 5 books).
P(5,5) = 5! / (5-5)! = 5! / 0! = 120
A committee of 3 people is to be selected from a group of 10. How many different committees can be formed?
There are 120 different ways to form the committee.
To find the number of combinations, we use the combination formula: C(n,r) = n! / [r!(n-r)!] Here, n=10 and r=3.
C(10,3) = 10! / [3!(10-3)!] = 10! / (3!7!) = 120
Find the number of ways to choose a president and a vice-president from a class of 8 students.
There are 56 different ways to choose the president and vice-president.
Choosing a president and a vice-president involves permutations (order matters). P(n,r) = n! / (n-r)!
Here, n=8 and r=2. P(8,2) = 8! / (8-2)! = 8! / 6! = 56
How many ways can you pick 4 different desserts from a menu of 8 options?
There are 70 different ways to pick the desserts.
To find the number of combinations, we use the combination formula: C(n,r) = n! / [r!(n-r)!]
Here, n=8 and r=4. C(8,4) = 8! / [4!(8-4)!] = 8! / (4!4!) = 70
In how many different ways can you arrange 4 out of 7 paintings on a wall?
There are 840 different ways to arrange the paintings.
To find the number of permutations, we use the permutation formula: P(n,r) = n! / (n-r)!
Here, n=7 and r=4. P(7,4) = 7! / (7-4)! = 7! / 3! = 840
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
: She has songs for each table which helps her to remember the tables