What is 24 factorial ?

The concept of factorial in mathematics refers to the product of all positive integers from 1 to a given number, symbolized by an exclamation mark. For example, the factorial of 24—or 24! —is significant as it represents the total number of ways to arrange 24 distinct items into a sequence. This concept is foundational in permutations, combinations, and various probability calculations, making it a cornerstone of discrete mathematics and other scientific fields.

To calculate the factorial of a number, we utilize the formula n! = n × (n-1) × … × 1. Applying this to the number 24, we calculate 24 factorial by multiplying all the integers from 24 to 1 sequentially. The calculation process begins with 24 and multiplies it by each preceding integer down to 1, which would look like this:

24! = 24 × 23 × 22 × … × 3 × 2 × 1

Calculating this results in a very large number indicating the vast number of ways to arrange 24 unique items.

The factorial of 24, amongst other factorial values, has various intriguing applications. In combinatorics, 24! represents the permutations of 24 items, central to calculating the probabilities in complex scenarios. In probability theory, it assists in determining chances within certain constraints. The factorial of 24 also emerges in algorithms and computational methods crucial for solving operations research problems and scheduling tasks. Understanding the factorial of 24 can therefore unlock solutions to real-world scenarios, including the organization of data in information technology.

• How many unique poker hand combinations can be made from a deck of 52 cards?
• If a soccer team has 24 players, in how many different ways can the coach select a captain and vice-captain?
• Imagine a shelf that can hold 24 books. How many different ways can you arrange 24 distinct books on this shelf?

• The number of unique poker hand combinations from 52 cards is calculated as 52! / (5! (52-5)!), which simplifies to 2,598,960 unique combinations.
• To select a captain and vice-captain from 24 players, you would calculate it as 24! / (2! (24-2)!), resulting in 552 possibilities.
• There are 24 factorial ways to arrange 24 books on a shelf, which equals the value of 24!, a vastly large number.