Let's say there are 11 places in a line where one can put boxes. How many options exist to place there 5 different sized boxes, when the order of the size is from smallest to largest?
The number of ways to choose k items (5) from n (11) distinct items, where the order of the items matters is: $\frac{n!}{(n-k)!}$.
But how can I adjust this number and consider only the orders that are strictly from smallest to largest? My idea was to just divide this number by $5!$. Is this valid?
Yes, dividing everything by k! will give you the number where the order has to be strictly from smallest to largest. As @Maximilian_Janisch said, the question is in fact equivalent to choosing 5 places out of 11 where order doesn't matter.
$\frac{n!}{ k! (n-k)!}$