Factorial/Examples/5

Example of Factorial

$5! = 120$


Proof

\(\ds 5!\) \(=\) \(\ds 5 \times 4 \times 3 \times 2 \times 1\) Definition 2 of Factorial
\(\ds \) \(=\) \(\ds 5 \times 4!\) Definition 1 of Factorial
\(\ds \) \(=\) \(\ds 5 \times 24\) Factorial of $4$
\(\ds \) \(=\) \(\ds 120\)

$\blacksquare$


Sources

  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 3$: The Binomial Formula and Binomial Coefficients: Factorial $n$
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