5!/3!*10!/7!

asked by guest
on Jan 22, 2025 at 8:03 am



You asked:

Evaluate the expression: \(\frac{\frac{5!}{3!} \cdot 10!}{7!}\)

MathBot Answer:

\[\frac{\frac{5!}{3!} \cdot 10!}{7!} = 14400\]

\[\begin{aligned}\frac{\frac{5!}{3!} \cdot 10!}{7!}& = 5! \cdot \frac{1}{3!} \cdot 10! \cdot \frac{1}{7!}\\& = 120 \cdot \frac{1}{3!} \cdot 10! \cdot \frac{1}{7!}\\& = \frac{120}{6} \cdot 10! \cdot \frac{1}{7!}\\& = \frac{120}{6} \cdot 3628800 \cdot \frac{1}{7!}\\& = \frac{120}{6} \cdot \frac{3628800}{5040}\\& = \frac{120}{6} \cdot 720\\& = 20 \cdot 720\\& = 14400\end{aligned}\]

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