Question

At an international conference, flags from 12 different countries will be displayed. Of these flags, 6 are from the continent of South America and 6 flags are from the continent of Europe. The flags will be displayed in a row, alternating between continents. A flag from South America will be in the first position. In how many ways can the flags be displayed?

Answer 1

Using the Fundamental Counting Theorem, it is found that the flags can be displayed in 518,400 ways.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem, we have that odd positions get South American countries, hence:

$n_1 = 6, n_3 = 5, n_4 = 3, \cdots, n_11 = 1$

Even positions get European countries, hence:

$n_2 = 6, n_4 = 5, \cdots, n_12 = 1$

Hence, since the number of ways for both the South American and European countries is the factorial of 6, we have that:

N = 6! x 6! = 518,400

The flags can be displayed in 518,400 ways.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866