(5! / 2!) * (7! / (2! * 2!))=

asked by guest
on Nov 15, 2024 at 10:39 am



You asked:

Evaluate the expression: \(\frac{5!}{2!} \cdot \frac{7!}{2! \cdot 2!}\)

MathBot Answer:

\[\frac{5!}{2!} \cdot \frac{7!}{2! \cdot 2!} = 75600\]

\[\begin{aligned}\frac{5!}{2!} \cdot \frac{7!}{2! \cdot 2!}& = 5! \cdot \frac{1}{2!} \cdot 7! \cdot \frac{1}{2! \cdot 2!}\\& = 120 \cdot \frac{1}{2!} \cdot 7! \cdot \frac{1}{2! \cdot 2!}\\& = \frac{120}{2} \cdot 7! \cdot \frac{1}{2! \cdot 2!}\\& = \frac{120}{2} \cdot 5040 \cdot \frac{1}{2! \cdot 2!}\\& = \frac{120}{2} \cdot 5040 \cdot \frac{1}{2 \cdot 2!}\\& = \frac{120}{2} \cdot 5040 \cdot \frac{1}{2 \cdot 2}\\& = \frac{120}{2} \cdot \frac{5040}{4}\\& = \frac{120}{2} \cdot 1260\\& = 60 \cdot 1260\\& = 75600\end{aligned}\]

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