What is the value of (6!-4!)?

Correct answer: (696)

A factorial is the product of all positive integers from the given number down to 1. Thus, the expression must be evaluated as a difference of two factorials: first calculate 6!, then calculate 4!, and finally subtract the smaller value from the larger one. It is important not to read 6!-4! as an ordinary difference inside a factorial; the factorial signs apply separately to 6 and 4.

We have \(6!=6\times5\times4\times3\times2\times1=720\), while \(4!=4\times3\times2\times1=24\). Therefore, \(6!-4!=720-24=696\). Hence option A is correct. The other numerical choices result from an arithmetic error or from mishandling one of the factorials.