Factorial as Product of Three Factorials/Examples/10

Example of Factorial as Product of Three Factorials

$10! = 7! \times 5! \times 3!$

Proof

\(\ds 10!\)

\(=\)

\(\ds 7! \times 6!\)

Factorial as Product of Two Factorials

\(\ds \)

\(=\)

\(\ds 7! \times \paren {3!}!\)

Definition of Factorial

\(\ds \)

\(=\)

\(\ds 7! \times \paren {3! - 1}! \times 3!\)

an instance of $\paren {n!}! = n! \paren {n! - 1}!$ from Factorial as Product of Two Factorials

\(\ds \)

\(=\)

\(\ds 7! \times 5! \times 3!\)

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3,628,800$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3,628,800$