10!/9!(10-9)!

asked by guest
on Nov 18, 2024 at 1:29 pm



You asked:

Evaluate the expression: \(\frac{10!}{9! \cdot \left( 10 - 9 \right)!}\)

MathBot Answer:

\[\frac{10!}{9! \cdot \left( 10 - 9 \right)!} = 10\]

\[\begin{aligned}\frac{10!}{9! \cdot \left( 10 - 9 \right)!}& = 10! \cdot \frac{1}{9! \cdot \left(10 - 9\right)!}\\& = 3628800 \cdot \frac{1}{9! \cdot \left(10 - 9\right)!}\\& = 3628800 \cdot \frac{1}{362880 \cdot \left(10 - 9\right)!}\\& = 3628800 \cdot \frac{1}{362880 \cdot 1!}\\& = 3628800 \cdot \frac{1}{362880 \cdot 1}\\& = \frac{3628800}{362880}\\& = 10\end{aligned}\]

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