[janemorales]

I am still having trouble - is this right? It seems to easy to be true.

Reynolds Construction Company has agreed not to erect all “look-alike” homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways can the exterior and interior plans be offered to potential home buyers?
There are 5 exterior designs and there are 3 interior designs.

5 exterior x 3 interior = 15 possible ways plans can be offered

[morgaine300]

Correct. It's a basic multiplication rule. You have two steps. First is picking the exterior and there are 5 possible outcomes for that. Second is picking an interior and there are 3 possible outcomes of that. And you just multiply them. If you think like a tree... there's 5 branches for the exteriors and each of those 5 still has 3 ways to make an interior. So you have 5 branches, with 3 branches coming off each, for 15 total.

Yes, it's that easy. One trick in probabilities is that sometimes something sounds really simple but it's complicated. And sometimes something seems complicated but it's very simple. I never quite trust the ones that seem simple. :-) But this one is. The reason this is simple is because it's just a two-step process. Picking an outside and then picking an inside. I always think of this like exterior AND interior. Am I going to do both? Yes. So that's my two steps. Now outcomes. 5 exteriors. Is that an AND? No, it's an OR. I will do only 1 of the 5. So the "or's" are the number of outcomes. So you follow along the steps (the AND's) and put down the number of possible outcomes for each. Then just multiply. This works whether the steps are the same or not. i.e. tossing a coin 2 times is not different. It's just the same step done twice. You do it the first time and you have 2 outcomes. You do it the second time, and you still have two outcomes. So 2 x 2. So don't think of that as being different. It's the same thing.

[Unknown008]

Ah no. There is permutations and combinations again. Here also, there're lots more different ways as all the five ex-design are different as the three in-design. In all, a house will have 8 designs, 3 ins and 5 exteriors. And notice the first line "not to erect all look alike homes". Therefore, the exterior and interior designs are kind of shuffled and put in different orders. So, you have 5! Times 3! (ie 5x4x3x2x1 x 3x2x1), which makes 720 ways!

[ebaines]

Jane - your answer is correct. Unknown's answer is not. One way to double-check your answer is to list out all the possible combinations. If we call the 5 exterior designs A, B, C , D, and E, and the 3 interior designs 1, 2, and 3, you can easily see that there are 15unique combinations of interior and exterior designs:

A1, A2, A3
B1, B2, B3,
C1, C2, C3
D1, D2, D3
E1, E2, E3

[Unknown008]

Ok, sorry, I misunderstood the problem... lol. My thought was that one home had 5 external designs and 3 internal designs... weird, yes I know! If you take the example of ebaines, then my first thought was a house with ABCDE123, ABCED123, etc. Ok, I'll try to do better next time.