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

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



You asked:

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

MathBot Answer:

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

20!⋅3!(22−2)!⋅2!=20!⋅3!⋅1(22−2)!⋅2!=2432902008176640000⋅3!⋅1(22−2)!⋅2!=2432902008176640000⋅6⋅1(22−2)!⋅2!=2432902008176640000⋅6⋅120!⋅2!=2432902008176640000⋅6⋅12432902008176640000⋅2!=2432902008176640000⋅6⋅12432902008176640000⋅2=2432902008176640000⋅64865804016353280000=2432902008176640000810967336058880000=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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