In mathematics, the exclamation mark (!) denotes the factorial function, which is the product of all positive integers up to a given number. In this article, we’ll know the concept of factorial and calculate the value of 9!.
What is 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. The factorial function is defined as:
n! = n × (n-1) × (n-2) × … × 2 × 1
For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
Calculating 9!
Now, let’s calculate the value of 9!:
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
To calculate this, we can start by multiplying the numbers in sequence:
9 × 8 = 72
72 × 7 = 504
504 × 6 = 3024
3024 × 5 = 15120
15120 × 4 = 60480
60480 × 3 = 181440
181440 × 2 = 362880
362880 × 1 = 362880
Therefore, the value of 9! is:
9! = 362880
Practical Applications of Factorial
The factorial function has numerous practical applications in mathematics, statistics, and computer science. Some examples include:
1. Permutations and Combinations: Factorial is used to calculate the number of permutations and combinations of a set of objects.
2. Probability Theory: Factorial is used in probability theory to calculate the probability of certain events.
3. Computer Science: Factorial is used in algorithms for solving problems related to permutations and combinations.
The factorial function is a fundamental concept in mathematics, and its applications are diverse and widespread. By understanding the factorial function, we can better appreciate the intricacies of mathematics and its practical applications in various fields.