Question

A dancing competition has 13 competitors, of whom four are American, two are Mexicans, four are Russians and three are Italians. If the contest result lists only the nationality of the competitors, how many outcomes are possible?

Answer 1

900,900 outcomes are possible.

Explanation:

Arrangements with repetition:

The number of possible arrangements of n elements, considered that they are divided in classes of
`n_1,n_2,...,n_n` elements, is given by:

`A = (n!)/(n_1!n_2!...n_n!)`

A dancing competition has 13 competitors

This means that
`n = 13`

Four are American, two are Mexicans, four are Russians and three are Italians.

This means that
`n_1 = 4, n_2 = 2, n_3 = 4, n_4 = 3`

How many outcomes are possible?

`A = (13!)/(4!2!4!3!) = 900900`

900,900 outcomes are possible.