Question

Evaluate the factorial of 5 ?

Answer 1

Hint: Factorial is the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. We must know beforehand that the factorial of $0$ is $1$ . So the factorial of a number $n$ is nothing but the product of all the numbers from $1$ till $n$. We will also multiply the number $n$ itself at the end. So here , our value of $n$ is $5$. So let us substitute it in place of $n$ and get the answer.

Complete step-by-step solution:
So we know that the factorial of a number $n$ is the product of all the numbers from $1$ till $n$.
Let us write it mathematically. We already know that we have to use the exclamation symbol to indicate the factorial of any number.
Upon doing so, we get the following :
$\Rightarrow n!=1\times 2\times 3........\times \left( n-1 \right)\left( n \right).$
We also know that the factorial of $0$ is $1$.
Let us write it mathematically also.
Upon doing so, we get the following :
$\Rightarrow 0!=1$
So now let us substitute the value of $n$ as $5$ to get the factorial of $5$.
Upon substituting, we get the following :
$\begin{align}
  & \Rightarrow n!=1\times 2\times 3........\times \left( n-1 \right)\left( n \right). \\
 & \Rightarrow 5!=1\times 2\times 3\times 4\times 5=120 \\
\end{align}$
We can find out the value of $6!$ by just multiplying $6$to $5!$.
$\therefore $ Hence, the value of factorial of $5$ is $120$.

Note: This chapter called Permutations and Combinations is a very tricky one. We should understand the logic behind each and every question so as to proceed further. We should memorize any formula without knowing any example of it or it’s application. To solve questions from this chapter quickly, a lot of practice is required. We should be careful while solving as there is a scope for a lot of logical and calculation errors.