1999 CEMC Gauss (Grade 8) Problems/Problem 13

Problem

The expression $n!$ means the product of the integers from $1$ to $n$ . For example, $5! = 1 \times 2 \times 3 \times 4 \times 5$ . The value of $6! - 4!$ is

$\text{ (A) }\ 2 \qquad\text{ (B) }\ 18 \qquad\text{ (C) }\ 30 \qquad\text{ (D) }\ 716 \qquad\text{ (E) }\ 696$

Solution 1

Using the definition of the factorial, we have $4! = 4 \times 3 \times 2 \times 1 = 12 \times 2 \times 1 = 24 \times 1 = 24$ , and $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 30 \times 4 \times 3 \times 2 \times 1 = 120 \times 3 \times 2 \times 1 = 360 \times 2 \times 1 = 720 \times 1 = 720$