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Q1(ii):
Evaluate (ii) $4! – 3!$
Solution :
Step 1: Theoretical Definition of Factorial
The factorial of a non-negative integer $n$, denoted by $n!$, is the product of all positive integers less than or equal to $n$. Mathematically, it is defined as:
$n! = n \times (n-1) \times (n-2) \times \dots \times 3 \times 2 \times 1$
[By the Fundamental Definition of Factorial Notation]
Step 2: Calculating $4!$
To evaluate the factorial of 4, we perform the following product:
$4! = 4 \times 3 \times 2 \times 1$
$4! = 24$
Step 3: Calculating $3!$
To evaluate the factorial of 3, we perform the following product:
$3! = 3 \times 2 \times 1$
$3! = 6$
Step 4: Performing the Subtraction
Substituting the computed values of $4!$ and $3!$ into the given expression $4! - 3!$:
Expression $= 24 - 6$
Expression $= 18$
Visual Representation of Factorial Growth
Final Solution: $4! - 3! = 18$
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