Question

How do you evaluate \[9!\]?

Answer 1

Hint: Here we have to evaluate \[9!\].This means we have to evaluate the factorial of nine. We will apply the formula which is used to find the factorial of a given number. In general, the formula for finding the factorial of a number is \[n!=n(n-1)(n-2)(n-3).............1\]. Here \[n\] is the number whose factorial we want to find. By substituting the value in the given formula, we will get the factorial of that number.

Complete step by step answer:
Before solving the question let us get familiar with the binomial expansion. We know that binomial is a polynomial that has only two terms in it and binomial expansion is expanding the binomial expression using binomial theorem. Here we have to find the factorial so factorial is basically the product of all the positive integers less than or equal to a given positive integer. It is represented by an exclamation mark “\[!\]”. The practical application of factorial is in permutations and combinations.
Now in this question, we have to find the factorial of nine. Thus, by substituting the value in the formula \[n!=n(n-1)(n-2)(n-3).............1\] we will get the value of \[9!\] .
The formula is \[n!=n(n-1)(n-2)(n-3).............1\]
Now we will substitute the value in the equation
\[\begin{align}
  & n!=n(n-1)(n-2)(n-3).............1 \\
 & \Rightarrow 9!=9(9-1)(9-2)(9-3).............1 \\
 & \Rightarrow 9!=9\times 8\times 7\times 6.............1 \\
 & \Rightarrow 9!=3628800 \\
\end{align}\]
Therefore, the value of \[9!\] is \[3628800\].

Note:
While we are finding the factorial, it is not mandatory to multiply with zero as \[0!=1\] therefore it will not affect the final value. The factorial formula is not applicable for negative integers. Keep in mind the formula used to find the factorial so that in the future you can easily solve questions of this type. Perform the calculations carefully.