Question

At an international conference, flags from 8 different countries will be displayed. Of these flags, 4 are from the continent of Africa and 4 flags are from the continent of Europe. The flags will be displayed in a row, alternating between continents. A flag from Africa will be in the first position. In how many ways can the flags be displayed?

Answer 1

The flags from 8 different countries, with 4 from Africa and 4 from Europe, can be displayed in a row in 576 different ways, given that a flag from Africa is in the first position and they alternate by continent.

Step-by-step explanation:

The student has asked how many ways the flags from 8 different countries can be displayed in a row, alternating between continents, with a flag from Africa in the first position. Since there are 4 flags from Africa and 4 from Europe, the arrangement will be Africa-Europe-Africa-Europe-Africa-Europe-Africa-Europe.

To solve this, we calculate the number of ways to arrange the African flags, which is 4! (factorial of 4), and the number of ways to arrange the European flags, also 4!. The total number of ways the flags can be displayed is the product of these two, so:

Total number of arrangements = 4! × 4! = (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1) = 24 × 24 = 576 ways.