What is 60 factorial ?

The concept of factorial pertains to a function in Mathematics that involves multiplying a series of descending natural numbers below a given number, down to 1. The factorial of 60, denoted as 60!, is particularly significant in mathematics due to its vast magnitude and its applications, which we’ll explore in subsequent sections. This sheer size of factorials for large numbers like 60 reflects the exponential growth rate and is crucial for solving combinatorial problems, among other uses.

The formula to calculate the factorial of a number is n! = n × (n-1) × … × 1. Here is how you apply the formula step by step to 60:

60! = 60 × 59 × 58 × … × 3 × 2 × 1

Calculating this manually is impractical because the result is a very large number. Instead, we use computational methods or factorial calculators to derive the value.

The factorial function has many robust applications in Mathematics. Factorial of 60 is often used in combinatorics, probability theory, and other mathematical fields to work with permutations and combinations of large data sets. It can also be significant in computing algorithms related to cryptography and coding theory where large-scale combinations of elements are analyzed.

• Consider an organization consisting of 60 members. Determine the total number of ways these members can be arranged in a line for a group photograph.
• If a class contains 60 students, in how many ways can a teacher form a committee of 5 members?

1. The total number of arrangements is the factorial of 60, i.e., 60!.
2. To form a committee of 5 from 60 students, we use combinations: C(60, 5) = 60! / (5! × (60 – 5)!).