Discrete Mathematics Calculators

Factorials, permutations, combinations, sequences and counting tools

Calculators

Pascal's Triangle Generator

Generate Pascal's Triangle for a selected number of rows.

Number of Rows

Pascal's Triangle

Each number is the sum of the two numbers directly above it.

C(n,r) = n! / [r!(n-r)!]

Fibonacci Numbers Calculator

Generate a Fibonacci sequence for a selected number of terms.

Number of Terms

Fibonacci Sequence

F₀ = 0
F₁ = 1
Fₙ = Fₙ₋₁ + Fₙ₋₂

Sandwich Combinations Problem

Calculate the number of possible sandwiches from a selected number of bread choices and filling choices.

Bread Choices

Filling Choices

Result

—

If one bread and one filling are selected:
Total Sandwiches = Bread Choices × Filling Choices

Factorial Calculator

n

Result

—

n! = n × (n−1) × (n−2) × ... × 1
0! = 1

Multifactorial Calculator

n

Step / Order k

Result

—

n!^(k) = n × (n−k) × (n−2k) × ...

Examples:
5! = 120
5!! = 15
5!!! = 5

Even Permutations Calculator

n

Result

—

Number of even permutations = n! / 2

Odd Permutations Calculator

n

Result

—

Number of odd permutations = n! / 2, n ≥ 2

Circular Permutation Calculator

Number of Objects n

Result

—

P(n) = (n − 1)!

Combinations Calculator

Order does not matter and repetitions are not allowed.

n

r

Result

—

nCr = C(n,r) = n! / [r!(n−r)!]

Order matters: No
Replacement allowed: No

Permutations Calculator

Order matters and repetitions are not allowed.

n

r

Result

—

nPr = P(n,r) = n! / (n−r)!

Order matters: Yes
Replacement allowed: No

Combinations with Replacement

Order does not matter and replacement is allowed.

n

r

Result

—

CR(n,r) = C(n+r−1,r)

Order matters: No
Replacement allowed: Yes

Permutations with Replacement

Order matters and replacement is allowed.

n

r

Result

—

PR(n,r) = nʳ

Order matters: Yes
Replacement allowed: Yes

Discrete Mathematics Calculators — Standalone HTML Tool