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

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by VJesus12 » Mon May 11, 2020 6:35 am
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\(\dfrac{12!}{3^4\cdot 5!\cdot 2^6}=\)

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

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT
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Re: \(\dfrac{12!}{3^4\cdot 5!\cdot 2^6}=\)

by Scott@TargetTestPrep » Wed May 13, 2020 8:16 am
VJesus12 wrote: ↑
Mon May 11, 2020 6:35 am
 \(\dfrac{12!}{3^4\cdot 5!\cdot 2^6}=\)

(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

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