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?

\({10 \choose 4} {6 \choose 3} {3 \choose 2}{1 \choose 1}\) = \(\frac{10!}{4! 3! 2! 1!}\)