#### Answer

90

#### Work Step by Step

If we look at the original fraction, $\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{8\times7\times6\times5\times4\times3\times2\times1}$, we can see there is actually no need to multiply together all the numbers in the numerator and the denominator. Rather, we can cancel.
The denominator is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Notice that 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 also appears in the numerator. As a result, we can cancel out this entire string of numbers from both the numerator and denominator. If we do this, we are left with 10 x 9, as the entirety of the denominator was cancelled out. 10 x 9 equals 90.