Find the value of 6!7! - 6!5! / 5!4!

Question

ScanSolve AI Tutor · Accepted Answer

To find the value of the expression, we will simplify the factorials.

Factor out the common term $6!$ from the numerator.
$\frac{6!7!-6!5!}{5!4!} = \frac{6!(7!-5!)}{5!4!}$
Expand $7!$ in terms of $5!$ in the numerator.
Recall that $7! = 7 \times 6 \times 5! = 42 \times 5!$ .
$\frac{6!(42 \times 5! - 5!)}{5!4!}$
Simplify the term in the parenthesis in the numerator.
$\frac{6!(42-1)5!}{5!4!} = \frac{6! \times 41 \times 5!}{5!4!}$
Cancel out $5!$ from the numerator and the denominator.
$\frac{6! \times 41}{4!}$
Expand $6!$ in terms of $4!$.
Recall that $6! = 6 \times 5 \times 4!$ .
$\frac{(6 \times 5 \times 4!) \times 41}{4!}$
Cancel out $4!$ from the numerator and the denominator.
$6 \times 5 \times 41$
Perform the multiplication.
$30 \times 41 = 1230$
The value of the expression is:
$\textbf{1230}$

Answer