Word Count : 395

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### Stirling’s Approximation: Stirling's approximation for factorials is given by: \[ n! \approx \sqrt{2\pi n} \left( \frac{n}{e} \right)^n \] where \( e \) is the base of the natural logarithm (\( e \approx 2.718 \)). ### Significance of Stirling's Approximation: - It provides an asymptotic estimate for large values of \( n \). - It simplifies factorial calculations, which grow rapidly. - It is useful in probability theory, combinatorics, and statistical mechanics. --- ### Computing \( 10! \) using Stirling’s Approximation: For \( n = 10 \): \[ 10! \approx \sqrt{2\pi \times 10} \times \left(\frac{10}{e}\right)^{10} \] #### Step _________ __________ __________ _____ _________ ____ ______ _____.
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