To determine the number of arrangements of a set of n objects when certain of the objects are indistinguishable (are alike) from each other
There are

Known as Multinomial Coefficient

A chess tournament has 10 competitors, of which 4 are Russian, 3 are from the US, 2 are from Canada, and one from Brazil. If the tournament results lists just the nationalities of the players in the order in which they placed, how many outcomes are possible?
$${10 \choose 4} {6 \choose 3} {3 \choose 2}{1 \choose 1}$$ = $$\frac{10!}{4! 3! 2! 1!}$$