The expression 6 x 5 x 4 x 3 x 2 x 1 represents the mathematical operation known as a factorial, specifically the factorial of the number 6. It is denoted as 6!.
In mathematics, the factorial of a non-negative integer is the product of all positive integers up to that number. Therefore, the expression can be calculated as follows:
- First, multiply 6 by 5: 6 x 5 = 30
- Next, multiply that result by 4: 30 x 4 = 120
- Then, multiply by 3: 120 x 3 = 360
- Now, multiply by 2: 360 x 2 = 720
- Finally, multiply by 1: 720 x 1 = 720
Thus, 6 x 5 x 4 x 3 x 2 x 1 = 720. This value, 720, represents the total number of ways to arrange 6 distinct objects. In practical terms, if you had 6 different books and wanted to know how many different ways you could line them up on a shelf, the answer would be 720.
Factorials are commonly used in various fields such as mathematics, statistics, and computer science, particularly in calculations involving permutations and combinations.