Bunuel wrote:

\(\frac{12!}{(3^4*5!*2^6)}=\)

(A) 2,210

(B) 770

(C) 480

(D) 77

(E) 35

Kudos for a correct solution.

\(\frac{12!}{(3^4*5!*2^6)}=\frac{(12*11*10*9*8*7*6*5!)}{(3^4*5!*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(12*11*10*9*8*7*6)}{(3^4*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(2^2*3*11*2*5*3^2*2^3*7*2*3)}{(3^4*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(2^7*3^4*11*5*7)}{(3^4*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(2*11*5*7)}{(1)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=(770)\)

Answer: Option

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