Ella makes a smoothie for breakfast every morning. Today, she wants to use melon, apple, orange, and peach. In how many different ways (orders) can she add these fruits to her blender?

( 1 ) We can apply factorial in this case. We have 4 elements, melon, apple, orange, and peach. The number of ways with which we have to arrange these fruits should be 4! ( again, there are 4 elements ).

4! = 4 [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1

4 [tex]*[/tex] 3 [tex]*[/tex] 2 [tex]*[/tex] 1 = 12 [tex]*[/tex] 2 [tex]*[/tex] 1

12 [tex]*[/tex] 2 = 24 different ways

( 2 ) The first method was the simpler approach. You can confirm this answer through another method...simply list out the different possibilities, altering their order in a specified manner.

{ melon, apple, orange, peach }

{ melon, apple, peach, orange }

{ melon, peach, apple, orange }...and keep on trying different combinations!