10!/9!(10-9)!

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



You asked:

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

MathBot Answer:

10!9!⋅(10−9)!=10\frac{10!}{9! \cdot \left( 10 - 9 \right)!} = 10

10!9!⋅(10−9)!=10!⋅19!⋅(10−9)!=3628800⋅19!⋅(10−9)!=3628800⋅1362880⋅(10−9)!=3628800⋅1362880⋅1!=3628800⋅1362880⋅1=3628800362880=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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