20!3!/(22-2)!2!

asked by guest
on Oct 29, 2024 at 10:24 pm



You asked:

Evaluate the expression: \(\frac{20! \cdot 3!}{\left( 22 - 2 \right)! \cdot 2!}\)

MathBot Answer:

\[\frac{20! \cdot 3!}{\left( 22 - 2 \right)! \cdot 2!} = 3\]

\[\begin{aligned}\frac{20! \cdot 3!}{\left( 22 - 2 \right)! \cdot 2!}& = 20! \cdot 3! \cdot \frac{1}{\left(22 - 2\right)! \cdot 2!}\\& = 2432902008176640000 \cdot 3! \cdot \frac{1}{\left(22 - 2\right)! \cdot 2!}\\& = 2432902008176640000 \cdot 6 \cdot \frac{1}{\left(22 - 2\right)! \cdot 2!}\\& = 2432902008176640000 \cdot 6 \cdot \frac{1}{20! \cdot 2!}\\& = 2432902008176640000 \cdot 6 \cdot \frac{1}{2432902008176640000 \cdot 2!}\\& = 2432902008176640000 \cdot 6 \cdot \frac{1}{2432902008176640000 \cdot 2}\\& = 2432902008176640000 \cdot \frac{6}{4865804016353280000}\\& = \frac{2432902008176640000}{810967336058880000}\\& = 3\end{aligned}\]

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