# [SOLVED]-aux.10.since he orders custom tiles how many choices does he have

#### karush

##### Well-known member
A tilesetter has 6 different stores where he buys tiles
each store has 6 different sizes of tiles
of these sizes there are 6 different types surfaces
of these surfaces there are 6 different types of designs
and last there 6 different types of mortor to use

since he orders custom tiles how many choices does he have

I came up with 4500

but do not have the proper equation to do this thanks ahead

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#### Plato

##### Well-known member
MHB Math Helper
A tilesetter has 6 different stores where he buys tiles
each store has 6 different sizes of tiles
of these sizes there are 6 different types surfaces
of these surfaces there are 6 different types of designs
and last there 6 different types of mortor to use
since he orders custom tiles how many choices does he have

I came up with 4500
QUESTION: Do any of the stores sell the same tiles?

I think that you need to explain in detail how you get that answer.

#### karush

##### Well-known member
QUESTION: Do any of the stores sell the same tiles?

I think that you need to explain in detail how you get that answer.
I see your point the intention was each store sold a different brand

#### Plato

##### Well-known member
MHB Math Helper
I see your point the intention was each store sold a different brand
Well you should have made that clear to begin with.
Now, how did you arrive at 4500?

#### HallsofIvy

##### Well-known member
MHB Math Helper
The "fundamental theorem of counting" says that if one event can happen in m ways and another can happen, independently, in n ways, then both can happen in m times n ways. In other words, because 6 stores he can choose from and each has 6 different kinds of files, there are 6(6)= 36 ways he can choose as store and a particular type of tile. As Plato asked, how did you arrive at 4500?

#### karush

##### Well-known member
Re: possiblilities(solved)

sorry everyone. my OP should be 5x6x5x6x5 which equals 4500
not 6x6x6x6x6
the original word problems had all the styles and types spelled out some with mulitple words so easy to miscount
4500 was the book ans.
yes I promise to be much more carefull about OP

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