How can (10!) be written using (8!)?

Correct answer: \(10\times9\times8!\)

Using the factorial rule, \(10!=10\times9\times8!\), because \(10!=10\times9\times8\times7\times\cdots\times1\) and \(8!=8\times7\times\cdots\times1\). Therefore, \(10\times9\times8!\) is correct. In \(10\times8!\), the factor \(9\) is missing. Exam tip: To express a larger factorial using a smaller one, multiply by the consecutive descending integers up to that smaller factorial.