\(\dfrac{12!}{3^4\cdot 5!\cdot 2^6}=\)

[VJesus12]

\(\dfrac{12!}{3^4\cdot 5!\cdot 2^6}=\)

(A) 2,210
(B) 770
(C) 480
(D) 77
(E) 35

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT

[Scott@TargetTestPrep]

\(\dfrac{12!}{3^4\cdot 5!\cdot 2^6}=\)

(A) 2,210
(B) 770
(C) 480
(D) 77
(E) 35

[spoiler]OA=B[/spoiler]

Canceling out 5! from the numerator and denominator, we have:
(12 x 11 x 10 x 9 x 8 x 7 x 6) / (3^4 x 2^6)

(2^2 x 3 x 11 x 2 x 5 x 3^2 x 2^3 x 7 x 2 x 3) / (3^4 x 2^6)

(2^7 x 3^4 x 5 x 7 x 11) / (3^4 x 2^6)

2 x 5 x 7 x 11

10 x 77

770

Answer: B