National and Regional Contests USA Contests USA - Middle School Tournaments Math Invitational for Girls 2019 MIG 12 2019 Individual #12 Problem Statement Calculate the product 1 3 × 2 4 × 3 5 × ⋯ × 18 20 × 19 21 \tfrac13 \times \tfrac24 \times \tfrac35 \times \cdots \times \tfrac{18}{20} \times \tfrac{19}{21} 3 1 × 4 2 × 5 3 × ⋯ × 20 18 × 21 19 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( A ) < / s p a n > 1 210 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( B ) < / s p a n > 1 190 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( C ) < / s p a n > 1 21 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( D ) < / s p a n > 1 20 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( E ) < / s p a n > 1 10 <span class='latex-bold'>(A) </span>\dfrac{1}{210}\qquad<span class='latex-bold'>(B) </span>\dfrac{1}{190}\qquad<span class='latex-bold'>(C) </span>\dfrac{1}{21}\qquad<span class='latex-bold'>(D) </span>\dfrac{1}{20}\qquad<span class='latex-bold'>(E) </span>\dfrac{1}{10} < s p an c l a ss = ′ l a t e x − b o l d ′ > ( A ) < / s p an > 210 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( B ) < / s p an > 190 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( C ) < / s p an > 21 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( D ) < / s p an > 20 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( E ) < / s p an > 10 1