Tedious Multiplication?

Relevant wiki: Multiplying Fractions

$\dfrac{\cancel{4}}{1}\times\dfrac{\cancel{5}}{2}\times\dfrac{\cancel{6}}{3}\times\dfrac{\cancel{7}}{\cancel{4}}\times\dfrac{\cancel{8}}{\cancel{5}}\times\dfrac{\cancel{9}}{\cancel{6}}\times\dfrac{\cancel{10}}{\cancel{7}}\times\dfrac{\cancel{11}}{\cancel{8}}\times\dfrac{\cancel{12}}{\cancel{9}}\times\dfrac{\cancel{13}}{\cancel{10}}\times\dfrac{\cancel{14}}{\cancel{11}}\times\dfrac{\cancel{15}}{\cancel{12}}\times\dfrac{\cancel{16}}{\cancel{13}}\times\dfrac{\cancel{17}}{\cancel{14}}\times\dfrac{18}{\cancel{15}}\times\dfrac{19}{\cancel{16}}\times\dfrac{20}{\cancel{17}}\\ =\dfrac{\color{#D61F06}{\cancel{\color{#333333}{18}}6}\times 19\times\color{#3D99F6}{\cancel{\color{#333333}{20}}10}}{1\times\color{#3D99F6}{\cancel{\color{#333333}{2}}1}\times\color{#D61F06}{\cancel{\color{#333333}{3}}1}}\\ =60\times 19\\ =\boxed{1140}$

$\displaystyle \frac{4\times 5 \times 6 \times \cdots \times 20}{1\times 2 \times 3 \times \cdots \times 17} = {20 \choose 17} = {20 \choose 3} = \frac {20 \times 19 \times 18}{1 \times 2 \times 3} = \boxed{1140}$

[20!/(3x2x1)] / 17! =1140