Question

What is the value of $4!$?

Answer 1

Hint: We first discuss the concept of factorial. We try to form the given multiplication starting from 1. We express the general form and use of the factorial. We multiply the remaining numbers to and find the factorial.

Complete step-by-step solution:
The given factorial is to be converted to the multiplication form. The use for the factorial function is to count how many ways you can choose things from a collection of things.
We know the term $n!$ defines the notion of multiplication of first n natural numbers.
This means $n!=1\times 2\times 3\times ....\times n$. But the multiplication has to start from 1.
Therefore, we multiply the terms from 1 to 4 for $4!$.
We get $4!=1\times 2\times 3\times 4=24$.

Note: These factorials are mainly used in cases of permutation or combination. In case of combination the simplified form of the mathematical expression ${}^{n}{{C}_{r}}$ is ${}^{n}{{C}_{r}}=\dfrac{n!}{r!\times \left( n-r \right)!}$. In case of permutation the simplified form of the mathematical expression ${}^{n}{{P}_{r}}$ is ${}^{n}{{P}_{r}}=\dfrac{n!}{\left( n-r \right)!}$. They are also used in probabilities.