Which statement best defines $n!$ ($n$ factorial)?

• A. The sum of all positive integers from $1$ to $n$, i.e., $1+2+\cdots +n$
• B. The product of all positive integers from $n$ down to $1$
• C. The number of combinations of $n$ objects taken at a time when order does not matter
• D. The sum of all positive integers from $1$ to $n$ multiplied by $n$, written as $(1+2+\cdots +n)n$

Answer: (B)