factorial

(noun)

The result of multiplying a given number of consecutive integers from $1$ to the given number. In equations, it is symbolized by an exclamation mark ($!$). For example, $5! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120$.

Related Terms

Examples of factorial in the following topics:

  • Binomial Expansion and Factorial Notation

    • The formula consists of factorials:
    • In calculating coefficients, recall that the factorial of a non-negative integer $n$, denoted by $n!
    • Finally, you may recall that the factorial $n!
    • Use factorial notation to find the coefficients of a binomial expansion

  • Permutations

    • In other words, a factorial is to multiply all the numbers from $1$ up to this number.
    • Instead of typing into a calculator six numbers to multiply, or sixty numbers or six hundred depending on the problem, the answer to a permutation problem can be found by dividing two factorials.
    • In many calculators, the factorial option is located under the "probability" menu for this reason.

  • Permutations of Nondistinguishable Objects

    • To correct for the "multiplicity" of certain permutations, we must divide the factorial of the total number of elements by the product of the factorials of the number of each repeated element.

  • Recursive Definitions

    • For example, the factorial function $n!

  • Application of Systems of Inequalities: Linear Programming

    • A factory makes three types of chairs, A, B, and C.
    • The factory makes a profit of $2 on chair A, $3 on chair B, and $4 on chair C.

  • Combinations