Question

12!4!÷15 como se calcula?

Answer 1

$\dfrac{12! \ 4!}{15} = \dfrac{(1*2*3*4*5*6*7*8*9*10*11*12)* \ 4!}{15} = \\ \\ \\ \dfrac{(1*2*\not 3*4*\not 5*6*7*8*9*10*11*12)* \ 4!}{\not 1\not 5} = \\ \\ \\ (1*2*4*6*7*8*9*10*11*12)* \ 4!=95800320 *(4!)= \\ \\ \\ 95800320*(24)= \boxed{2299207680}$


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$\dfrac{12! \ 4!}{15! } = \dfrac{(12!)* \ 4!}{15*14*13*12!} = \dfrac{ \ 4!}{15*14*13} = \dfrac{ 4*3*2*1}{15*14*13} = \\ \\ \\ \dfrac{ 24}{15*14*13} = \dfrac{ 8}{5*14*13} =\dfrac{ 4}{5*7*13} = \boxed{\dfrac{ 4}{455}}$