Question

(78) The flag of country Perralia has to contain three differently-colored stripes of the same width, all of which must be positioned either vertically or horizontally. If the flag of Perralia must consist of the national colors, which include green, red, yellow, black, and blue, how many different flags can be created

Answer 1

120 flags

Explanation:

Given that:

The flag of country Perralia has to contain three differently-colored stripes of the same width, r = 3 stripes

all of which must be positioned either vertically or horizontally = 2

If the flag of Perralia must consist of the national colors, which include green, red, yellow, black, and blue. So the number of color n = 5 colors

The objective is to determine how many different flags can be created.

Let us recall that;the arrangement of objects taking into account the different orders or arrangement is called permutation.

The same is applicable in this scenario as well.

The number of flags that can be created can be determined by considering the permutation of :

`P_r = (n!)/((n-r)!)`

`P_r = (5!)/((5-3)!)`

`P_r = (5!)/((2)!)`

`P_r = (5 * 4 * 3 * 2!)/((2)!)`

`P_r = {5 * 4 * 3`

`P_r = 60`

However, Since all of the must be positioned either vertically or horizontally = 2

Then the total number pf flags that be created = 2 × 60 = 120 flags