Factorials and Combinations I understand that $$n! = n (n-1) (n-2)\cdots 2 \cdot 1.$$ My book says this can also be written as $$n (n-1)!$$ Without telling me why
My question is How and why is that? Why can't we leave it as it is? Basically looking for an easy to understand explanation.
Thank You

I want to add that understanding what factorials represent, combinatorially, is another way of understanding where the second formula 'comes from'.  Remember that $n!$ is the number of ways of arranging $n$ distinct objects (say, pool balls numbered $1\ldots n$) in a line; now consider the ball labeled $n$.  There are $n$ 'places' that it can go in the line; the first slot, the second slot, ..., all the way to the $n$th slot.  And wherever you take it out from the line, the other $(n-1)$ balls can be arbitrarily arranged in $(n-1)!$ ways, so the total number of arrangements $n!$ must be the same as the product (places to put the $n$th ball)$\times$(ways of arranging the other balls) - or in other words, $n\times(n-1)!$.
