What is the expression for calculating the factorial of a number n?

The factorial of a number ( n ), denoted as ( n! ), is defined as the product of all positive integers from ( n ) down to ( 1 ). This means that to calculate ( n! ), you multiply ( n ) by every integer that is less than ( n ) until you reach ( 1 ). The expression provided reflects this definition accurately.

So, if you have a number, let’s say ( 5 ), the factorial ( 5! ) would be calculated as ( 5 \times 4 \times 3 \times 2 \times 1 ). This aligns perfectly with the described expression ( n(n-1)(n-2)...(2)(1) ), where you continue multiplying by each preceding integer until you reach 1.

The other options given involve different mathematical concepts. For instance, options involving ( n! ) divided by any factorials relate to combinations or permutations, where factors represent selections or arrangements from a set, which do not apply to the factorial definition directly. Therefore, recognizing that ( n! ) specifically represents the product of the sequence back to 1 is key to understanding why the correct expression is the one