Why 117+3 = 5! is correct
The Correct Answer and Explanation is:
The equation “117 + 3 = 5!” involves two different mathematical concepts: simple arithmetic and the factorial operation. Let’s break it down to understand why it holds true.
- Addition (117 + 3):
The first part of the equation involves basic addition. When you add 117 and 3, you get:
[
117 + 3 = 120
]
So, the left side of the equation simplifies to 120. - Factorial (5!):
The second part of the equation is the factorial of 5, written as (5!). The factorial of a number is the product of all positive integers from 1 up to that number. For (5!), you calculate:
[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
]
Therefore, (5! = 120). - Equality:
Now, comparing both sides of the equation:
- Left side: (117 + 3 = 120)
- Right side: (5! = 120) Since both sides equal 120, the equation is indeed correct.
Explanation:
The equation (117 + 3 = 5!) holds true because both the sum of 117 and 3, and the factorial of 5, simplify to the same value, 120. The factorial notation is an important concept in mathematics, often used in combinatorics, probability theory, and algebra, to represent the product of a series of descending positive integers. In this equation, the factorial operation gives a quick way to arrive at the same result as the simple addition.
Thus, the equation is correct because both sides result in the same numerical value (120). This demonstrates an interesting relationship between a basic arithmetic operation (addition) and a more advanced operation (factorial), both of which can lead to the same result in this particular case.