Question

In this question we need to find the factorial of $5$. To solve this we need to know how to perform multiplication of two numbers and its properties. In this question to find the factorial of a number we just have to multiply all numbers less than that number and greater than equal to $1$.

Answer 1

Hint:In this question we need to find the factorial of $5$. To solve this we need to know how to perform multiplication of two numbers and its properties. In this question to find the factorial of a number we just have to multiply all numbers less than that number and greater than equal to $1$.

Complete step by step solution:
Let us try to solve this question in which we are asked to find the factorial of $5$. Before solving this we first define the factorial of a number. Factorial of a number $n$is defined as the product of the first $n$ natural number i.e., $1 \times 2 \times 3 \times ... \times (n - 1) \times n$and denoted by $n!$ . We have a special case factorial $0$ is equal to $1$. For example a factorial of $3$ is equal to $6$. Now coming back to our question we find a value of $5!$.
By using the definition of factorial of a number, we write $5!$ as
$5! = 1 \times 2 \times 3 \times 4 \times 5$
Now by using associative property of multiplication, we get
$
5! = (1 \times 2) \times (3 \times 4) \times 5 \\
\,\,\,\,\, = (2 \times 12) \times 5 \\
\,\,\,\,\, = 24 \times 5 \\
\,\,\,\,\, = 120 \\
\,\,\,\,\, \\
$
Hence the value of $5!$ is equal to $120$.

Note: This question is very easy to do and generally asked for very short answer type questions. Factorial of a number greater than $4$ has at least one $0$ in its factorial. Factorial of a number is used in permutation and combination both are ways of counting. Permutation and combination are used to solve problems on probability. Hence knowing how to find the factorial of a number is very important, because it is heavily used in the most important topics of mathematics such as permutation, combination and probability.