What is 52 factorial ?

Factorial, indicated by the symbol ‘!’, represents the product of all positive integers up to a given number. The factorial of 52, denoted as 52!, is especially significant in mathematics due to the vast number of permutations it can express, given its relation to combinatorial problems and probability calculations.

The calculation for 52 factorial follows the formula n! = n × (n-1) × … × 1. For the number 52, it entails multiplying every natural number from 52 down to 1. As a concrete example, the initial steps would look like 52 × 51 × 50 × … × 3 × 2 × 1.

The factorial of 52 can be particularly notable in areas like combinatorics, where it can represent the number of ways to order a deck of cards. It also surfaces in probability theory and can be seen in algorithms that rely on understanding the total possible permutations of a set.

• How many distinct arrangements can be made using all cards in a standard deck?
• If you were to take one card out of a deck, how many arrangements would be possible with the remaining cards?

1. Since a standard deck contains 52 cards, the number of different arrangements is equal to 52!, which is a substantial number beyond the scope of manual calculation.
2. With one card removed, 51 cards remain, thus the number of distinct arrangements is 51!.