What is 25 factorial ?

The concept of a factorial in mathematics refers to the product of all positive integers up to a certain number, denoted by the symbol “n!”. This function plays a crucial role in various mathematical disciplines such as combinatorics and probability theory. When we speak of 25 factorial, symbolized as “25!”, we are referring to the multiplication of all numbers from 1 to 25. This massive number is fundamental in calculating permutations and combinations, where the order and arrangement of things are studied.

To calculate the factorial of any number, including 25, we use the basic formula: n! = n × (n-1) × … × 3 × 2 × 1. Applying this to 25 factorial:

25! = 25 × 24 × 23 × … × 3 × 2 × 1

This operation involves a lengthy multiplication sequence, with the final result being an extremely large number that’s typically beyond everyday comprehension but holds significant value in mathematical calculations.

The factorial function, especially when calculated for large numbers like 25, is used in various scientific and mathematical fields. In combinatorics, 25! is pivotal in determining the number of possible arrangements of 25 distinct objects. In probability theory, it assists in solving problems related to complex distributions and event occurrences. Moreover, factorials are used in algorithms within computer science to handle data arrangements and optimizations.

• Exercise 1: Calculate the last two digits of 25 factorial.
• Exercise 2: If you have 25 different books, in how many ways can you arrange them on a shelf?
• Exercise 3: What is the ratio of the factorial of 25 to that of 24?

• Solution 1: With 4 trailing zeros in 25 factorial, the last two non-zero digits are 57.
• Solution 2: The number of ways to arrange 25 books is the same as 25 factorial, which is a very large number.
• Solution 3: The ratio is 25, since 25! / 24! is simplified to 25.