6!/1!(6-1)! times 8!/2!(8-2)!

asked by guest
on Jan 27, 2025 at 5:06 am



You asked:

Evaluate the expression: \(\frac{6!}{1! \cdot \left( 6 - 1 \right)!} \cdot \frac{8!}{2! \cdot \left( 8 - 2 \right)!}\)

MathBot Answer:

\[\frac{6!}{1! \cdot \left( 6 - 1 \right)!} \cdot \frac{8!}{2! \cdot \left( 8 - 2 \right)!} = 168\]

\[\begin{aligned}\frac{6!}{1! \cdot \left( 6 - 1 \right)!} \cdot \frac{8!}{2! \cdot \left( 8 - 2 \right)!}& = 6! \cdot \frac{1}{1! \cdot \left(6 - 1\right)!} \cdot 8! \cdot \frac{1}{2! \cdot \left(8 - 2\right)!}\\& = 720 \cdot \frac{1}{1! \cdot \left(6 - 1\right)!} \cdot 8! \cdot \frac{1}{2! \cdot \left(8 - 2\right)!}\\& = 720 \cdot \frac{1}{1 \cdot \left(6 - 1\right)!} \cdot 8! \cdot \frac{1}{2! \cdot \left(8 - 2\right)!}\\& = 720 \cdot \frac{1}{1 \cdot 5!} \cdot 8! \cdot \frac{1}{2! \cdot \left(8 - 2\right)!}\\& = 720 \cdot \frac{1}{1 \cdot 120} \cdot 8! \cdot \frac{1}{2! \cdot \left(8 - 2\right)!}\\& = \frac{720}{120} \cdot 8! \cdot \frac{1}{2! \cdot \left(8 - 2\right)!}\\& = \frac{720}{120} \cdot 40320 \cdot \frac{1}{2! \cdot \left(8 - 2\right)!}\\& = \frac{720}{120} \cdot 40320 \cdot \frac{1}{2 \cdot \left(8 - 2\right)!}\\& = \frac{720}{120} \cdot 40320 \cdot \frac{1}{2 \cdot 6!}\\& = \frac{720}{120} \cdot 40320 \cdot \frac{1}{2 \cdot 720}\\& = \frac{720}{120} \cdot \frac{40320}{1440}\\& = \frac{720}{120} \cdot 28\\& = 6 \cdot 28\\& = 168\end{aligned}\]

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