Question

New Ta Help Sa Chapter 4 Assignment 6 Construction Company has agreed not to erect look-alike homes in a new subdivision Five exterior designs are offered to potential home buyers. The builder has standerdized three interor plans thet can be incorporated in any of the five exteriors How many different ways can the exterior and Number of diferent ways interior plans be offered to potential home buyers t0

Answer 1

There are 5 types of exterior designs for homes. Lets say they are numbered 1, 2, 3, 4 & 5. Each of these homes can have 3 interior designs, lets say A , B & C.

Now, house with exterior design 1 can have any one of the 3 interior designs. Similarly, house with exterior design 2 can have any one of the 3 interior designs & so on.

Exterior design	Interior design
1	A
	B
	C
2	A
	B
	C
3	A
	B
	C
4	A
	B
	C
5	A
	B
	C

So, each of these 5 exteriors can be offered in 5 different ways & each one of these can be paired with any one of the 3 interiors in 3 different ways.

So, the total number of ways these can be offered are 3*3*3*3*3 = $3^{5}$ = 243