Question

Enzo is buying wallpaper. He can choose one colour, one texture and one thickness for his wallpaper. At his local DIY store, Enzo can choose from 27 different colours 14 different textures. The total number of options available to enzo for his wallpaper is 2268. Work out the number of different wallpaper thicknesses that enzo can choose from.

Answer 1

6 different wallpapers

Explanation:

Given

`Colours = 27`

`Textures = 14`

`Total = 2268`

Required

Determine the number of different wallpapers he can choose from

From the question, he can choose 1 from 27 colors;

The number of ways is:

`Colours = ^(27)C_1 = (27!)/((27 - 1)!*1!) = (27!)/(26!*1!) = = (27*26!)/(26!*1) = 27`

From the question, he can choose 1 from 14 textures;

The number of ways is:

`Textures = ^(14)C_1 = (14!)/((14 - 1)!*1!) = (14!)/(13!*1!) = (14*13!)/(13!*1) = 14`

Assume the total number of wallpapers is x and he can only select 1.

The number of ways of selection is:

`Wallpapers = ^(x)C_1 = (x!)/((x - 1)!*1!) = (x* (x - 1)!)/((x - 1)!*1!) = x`

So, the total selection is:

`Colours * Textures * Wallpapers = Total`

`27 * 14* x= 2268`

`378* x= 2268`

Divide both sides by 378

`(378* x)/(378)= (2268)/(378)`

`x= (2268)/(378)`

`x= 6`

Hence, the number of different wallpaper is 6