What mathematical concept is defined as the product of all whole numbers less than or equal to a number?

The concept being described, where the product of all whole numbers less than or equal to a number is taken, is known as the factorial. For a given non-negative integer ( n ), the factorial is denoted by ( n! ) and is calculated as ( n \times (n - 1) \times (n - 2) \times ... \times 3 \times 2 \times 1 ). For example, ( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 ). This distinction makes factorial a fundamental concept in combinatorics, particularly in permutations and combinations, where arrangements of items need to be calculated.

The other options do not accurately represent this definition. The sum refers to the addition of numbers rather than their product. Integral usually pertains to calculus and areas under curves or summing infinitely many infinitesimal quantities, while product generally refers to multiplication but does not specify the sequence of whole numbers leading up to a certain integer. Therefore, factorial encompasses the specific process of multiplying a sequence of numbers down to one, making it the correct answer.