we are given
A furniture manufacturer offers bookcases in 5 different sizes
so, number of bookcases of different size =5
A furniture manufacturer offers bookcases in 3 different colors
so, number of bookcases of different colors =3
since, every color is available in every size
so,
total number of different bookcases=(number of bookcases of different size)*(number of bookcases of different colors)
now, we can plug values
and we get
total number of different bookcases=5*3
So, total number of different bookcases is 15 ............Answer