What is 150 factorial ?

The concept of a factorial in mathematics refers to the product of a series of descending natural numbers down to one. For larger numbers like 150, although calculating the factorial overtly would be impractical due to the enormity of the number produced, understanding its properties is crucial for grasping complex mathematical theories. Essentially, the factorial for such large numbers serves as a theoretical tool in understanding concepts of permutations, combinations, and probability.

The factorial of a number n is defined as n! = n × (n−1) × … × 1. To calculate the factorial of 150, you would theoretically multiply 150 by every number less than it down to 1. Given the large size of this calculation, a concrete step-by-step example is not practical here, but the process is consistent with the factorial definition.

The factorial of large numbers like 150 have significant applications in various mathematical fields. In combinatorics, 150! delineates the number of ways to arrange 150 distinct objects. In probability theory, it helps calculate the likelihood of certain outcomes. The factorial is also vital in series expansions and computations in higher calculus and analysis, dealing with extremely large datasets.

• What is the last non-zero digit of 150!
• Given a standard deck of playing cards, in how many ways can one draw a subset of 150 cards?

The last non-zero digit of 150! is a complex problem that involves understanding trailing zeros and carrying operations in multiplication. Such a calculation for large numbers is typically done through programming rather than by hand.

The combinatorial question involving a deck of cards is a trick question as there are only 52 cards in a standard deck. It is not possible to draw a subset of 150 cards from a 52-card deck.