Operation Definition Problem

9. a ve b pozitif doğal sayılar olmak üzere

$$\begin{matrix} \\ \boxed{a} \\ \blacktriangle_{b} \end{matrix} = a \cdot (a+1) \cdot (a+2) \cdots (a+b)$$

$$\begin{matrix} \boxed{a} \\ \blacktriangledown_{b} \end{matrix} = a \cdot (a-1) \cdot (a-2) \cdots (a-b)$$

işlemleri tanımlanıyor.

Buna göre

$$\frac{\begin{matrix} \boxed{20} \\ \blacktriangledown_{19} \end{matrix}}{\begin{matrix} \blacktriangle_{4} \\ \boxed{16} \end{matrix}} - 4!$$

işleminin sonucu hesaplandığında elde edilen sayının son üç basamağındaki rakamların toplamı kaçtır?

A) 22

B) 21

C) 20

D) 19

E) 18

Soruda görsel içerik var: The image defines two custom operations using geometric symbols. The first is an orange rectangle with a triangle pointing up (labeled b) on top, equal to a*(a+1)*(a+2)...*(a+b). The second is a blue rectangle with a triangle pointing down (labeled b) on bottom, equal to a*(a-1)*(a-2)...*(a-b). A complex expression is provided: a fraction with a blue shape containing 20 above a downward triangle containing 19 in the numerator, and an orange shape containing 16 above an upward triangle containing 4 in the denominator, followed by the subtraction of 4!.