Discrete Mathematics Calculators

Have a look at the simple guidelines to follow in order to solve the problems in Discrete Mathematics. Following them, you can arrive at the solution easily. They are along the lines.

• Consider the values n, r from the given data.
• Know the different formulas for discrete mathematics and substitute the input data in them.
• Perform basic math calculations required and get the result easily.

Discrete Mathematics includes topics like Factorial, Even, Odd, Circular Permutations, Combinations, Permutations, Permutations Replacement, Combinations Replacement, etc. We have covered all the formulas for the related concepts in the coming sections. They are as such

Factorial

Factorial is a function that multiplies the number by every number below it and is denoted by the exclamation mark symbol. The formula for finding factorial is n!

Factorial = n! = n*(n-1)!

Even Permutations

You can determine the Even Permutations for a given set of numbers easily. The formula for finding the Even Permutations of a given set is n!/2 for n> 2. You can simply substitute the value of n in the formula and then find the even permutation easily.

Even Permutations = n!/2 for n> 2

Odd Permutations

For a set of n elements, there exists n!/2 for n>=2 Odd Permutations. Substitute the value of n in the formula and perform required calculations to get the Odd Permutations effortlessly.

Odd Permutations = n!/2 for n>= 2

Circular Permutations

In general, Circular Permutations is nothing but arranging distinct objects around a fixed circle. Circular Permutation is given by the formula (n-1)!. Plugin the value of n given and solve to get the number of ways you can arrange distinct objects around a circle.

P(n) = (n-1)!

Combinations

A combination is nothing but the number of ways in which you can select r elements out of a set containing n objects where order doesn’t matter and repetitions are not allowed. It might be difficult to write all the possible sets thus we have provided a simple formula to calculate the different combinations.

ⁿC_r = C(n,r) = n!/(r! (n-r)!)  where n is the total number of elements in the set and r is the number of elements chosen from the set.

Permutations

A permutation is a number of ways in which you can select r elements out of a set containing n distinct objects in which order matters. Make use of the formula below to calculate the Permutations in a matter of seconds.

P(n,r) = n!/(n-r)! for n ≥ r ≥ 0

where P is the number of permutations in the set, n is the total number of elements in the set and r is the total number of items you choose from the set.

Combinations Replacement

This is the case of Combinations in which Repetitions are allowed. In fact, each time you pick an element you put it back to the set. The formula to calculate Combinations Replacement is given by

C^R(n, r) or C'(n,r) = (r+n-1)!/(r! * (n-1)!)

Where C'(n,r)) is the number of combinations with repetition or replacement, n is the total number of elements in the set, and r is the number of elements you choose from this set.

Permutations Replacement

In the case of Permutations Replacement, a sample of r elements is taken from a set of n distinct objects, order matters, and replacements are allowed.

P^R(n,r)=n^r

Where p is the number of permutations, n is the total number of elements in the set, and r is the number of elements you choose from this set.

Example: Calculate Discrete Mathematics for n = 5, r = 2?

Solution:

Given n= 5, r = 2

Factorial

Formula for Factorial is n!

Place the value of n i.e. 5

Factorial = 5!

= 5*4*3*2*1

= 120

Even Permutations

Even Permutations = n!/2 for n> 2

Placing the value of n= 5 we get

= 5!/2

=60

Odd Permutations

Odd Permutations = n!/2 for n>=2

Substitute the value of n we get the equation as under

= 5!/2

=60

Circular Permutations

Circular Permutations P(n) = (n-1)!

= (5-1)!

= 4!

= 24

Combinations

Formula for Combinations is ⁿC_r = C(n,r) = n!/(r! (n-r)!)

⁵C₂ = 5!/(2!(5-2)!)

= 5!/(2!*3!)

= 10

Permutations

Formula for Permutations is P(n,r) = n!/(n-r)! for n ≥ r ≥ 0

Substitute the value of n, r i.e. 5 and 2 in the formula

P(5, 2) = 5!/(5-2)!

= 5!/3!

= 20

Combinations Replacement

The formula for Combinations Replacement is C'(n,r) = (r+n-1)!/(r! * (n-1)!)

Placing the values of n, r i.e. 5 and 2 in the above formula we get

C'(5,2) = (2+5-1)!/(2!*(5-1)!)

= 6!/2!*4!

=21

Permutations Replacement

The formula for Permutations Replacement is P^R(n,r)=n^r

P^R(5, 2)= 5²

= 25

Take help regarding several math concepts that seemed difficult to you using the online tools available at Onlinecalculator.guru and clear all your queries.

1. What is the best way to learn Discrete Mathematics?

The best way to learn Discrete Mathematics is to practice the concepts underlying on a regular basis.

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2. How to use Discrete Mathematics Calculators?

Just enter the input values in the corresponding input sections and click on the calculate button to avail the result in no time.

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3. What Concepts of Discrete Mathematics is supported by this tool?

The tool over here supports Discrete Mathematics concepts like Factorial, Even, Odd, Circular Permutations, Combinations, Permutations, Combinations Replacement, Permutations Replacement.

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4. Where do I get Formulas to solve problems on Discrete Mathematics?

You can get Formulas to solve problems on Discrete Mathematics all on our page.

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