What is 32 factorial ?

A factorial is a mathematical operation designated by an exclamation point “!” that signifies the product of a series of descending natural numbers from a chosen number down to one. For instance, the factorial of 32, denoted as 32!, is a particularly large number used in various branches of mathematics. Understanding the factorial of 32 is significant for enumerating possibilities in combinatorial problems and calculating probabilities, among other advanced mathematical concepts.

The factorial function can be defined by the formula n! = n × (n-1) × … × 3 × 2 × 1. To find the factorial of 32, you would perform a multiplication operation starting with 32 and decrementing by one each time, continuing down to the number one. The series would begin with 32, followed by 31, 30, and so forth, until reaching one and multiplying all these numbers together. The calculation is extensive, as 32! results in a very large number.

The factorial of 32 has several intriguing applications in different areas of mathematics. In combinatorics, it is used to determine the number of ways to arrange 32 distinct objects. It also plays a pivotal role in probability theory when calculating the odds of specific outcomes. Additionally, the factorial function is involved in algorithms and formulas such as those found in algebra, numerical analysis, and computer science, where 32! might emerge in the analysis of algorithms or the solving of complex equations.

• Calculate the last two digits of 32! without computing the whole factorial.
• If you have a set of 32 unique cards, in how many ways can you distribute them in four stacks of eight cards each?

1. Since there are multiple of 10 within the first 32 numbers, the last two digits of 32! would be 00.
2. The number of ways to distribute 32 unique cards into four stacks of eight can be calculated as the division of the factorial of 32 by the product of the factorial of 8 four times, (32!)/(8!)^4.