Chapter 12.CR, Problem 1CR

To determine

To simplify:

The value of the expression $8!-3!$.

Answer to Problem 1CR

Solution:

$40,314$.

Explanation of Solution

Definition:

For any counting number n, the factorial of n is defined as,

$n!=n\left(n-1\right)\left(n-2\right)\mathrm{....3}\cdot 2\cdot 1$

Calculation:

Consider the provided expression $8!-3!$.

Use the formula for factorial to evaluate the factorials separately and find the difference. So,

$\begin{array}{rll}8!-3!& =& \left(8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\right)-\left(3\cdot 2\cdot 1\right)\\ & =& 40,320-6\\ & =& 40,314\end{array}$

Thus, the simplified value of the provided expression is $40,314$.

Final statement:

The expression $8!-3!$ simplifies to $40,314$.