# Thread: I Need Help With Factors

1. ## I Need Help With Factors

So I Know Nothing About Math And I Need To Get This Done. Here Is The Problem

I Have A Footprint Of A House. And There Are 7 Options That Could Change That Footprint. So How Many Footprints Can There Be Total?

1 Footprint
7 Options

You Cannot Use The Same Option. So If I Used Option A And Added Option B, When It Comes To Figure Out The Options On B I Cant Use A. Make Sense? I Think The Answer Is 148 But Im Not Sure. Please Help Anyone.

2. Hello, HVRIDERZ!

I know nothing about a footprint of a house . . . what is it?

I Have A Footprint Of A House.
And There Are 7 Options That Could Change That Footprint.
So How Many Footprints Can There Be Total?

For each option, there are two choices: apply it or don't apply it.

Hence, there are: $2^7 = 128$ possible options
. . from "use none of them" to "use all of them".

3. Originally Posted by HVRIDERZ
So I Know Nothing About Math And I Need To Get This Done. Here Is The Problem

I Have A Footprint Of A House. And There Are 7 Options That Could Change That Footprint. So How Many Footprints Can There Be Total?

1 Footprint
7 Options

You Cannot Use The Same Option. So If I Used Option A And Added Option B, When It Comes To Figure Out The Options On B I Cant Use A. Make Sense? I Think The Answer Is 148 But Im Not Sure. Please Help Anyone.

If I understand it correctly you want find every possible different combinations of options to apply on footprint.

So, you have:
7/1 = 7
7*6/1*2 = 21
7*6*5/1*2*3 = 35
7*6*5*4/1*2*3*4 = 35
7*6*5*4*3/1*2*3*4*5 = 21
7*6*5*4*3*2/1*2*3*4*5*6 = 7
7*6*5*4*3*2*1/1*2*3*4*5*6*7 = 1

Add all those results:
7+21+35+35+21+7+1=127 total options.

Total 128 various footprints (127 with different options and one footprint without applying any option).

4. Originally Posted by Soroban
Hello, HVRIDERZ!

I know nothing about a "footprint of a house" . . . what is it?

For each option, there are two choices: apply it or don't apply it.

Hence, there are: $2^7 = 128$ possible results,
. . from "use none of them" to "use all of them".

Deja vu

5. ok a footprint of a house is the perimeter of a house. so take the house u live in and measure all the outside walls, then draw it on a piece of paper and you will have a footprint.

so one factor i forgot to mention, 2 options cant be used together. just some info: the option is a 2' garage extention and a 4' garage extention. so clearly you can only have one or the other. what would be the formula to finding that out.

6. Originally Posted by HVRIDERZ
ok a footprint of a house is the perimeter of a house. so take the house u live in and measure all the outside walls, then draw it on a piece of paper and you will have a footprint.

so one factor i forgot to mention, 2 options cant be used together. just some info: the option is a 2' garage extention and a 4' garage extention. so clearly you can only have one or the other. what would be the formula to finding that out.
Subtract from number 128 possible combinatios of that two options that can't be together with other options.

Let's say you have options A,B,C,D,E,F,G so that F,G can't be together in any combination.

We have already counted total number of options (and with no options) which is 128.

So, we must find total number of combinations where F,G are together.
That is total of 32 combinations where F,G are together.

That is 128 - 32 = 96 of total options.

7. can you tell me how you figured out 32? the only thing i came up with was 2^5 and that equals 23. but what is the reasoning for that?

i drew it up and came up with 96, now if i use the same thing as you did of 2^5 and try to simplify the same situation so now i have 4 options or in this case now known as (G,F,E,D,) so this is the deal. G and F can never be together. same goes for E and D. however G can be with E or D but not the 2 together. hopefully all that makes sense.im trying to get a formula to do it so i can proceed with my work. thanks