## Related questions with answers

The Fitzgeralds are installing inground pool in their back yard. They can either install the base model offered by the pool company or add any of the following options: automatic pool cleaner, solar cover, waterfall, hot tub, fountain, slide, diving board. How many different variations of the pool are possible?

Solutions

VerifiedLet $A$ be the set of all options that the Fitzgeralds can add to the base model of the pool,

Then,

{$A=\text{automatic pool cleaner, solar cover, waterfall, hot tub, fountain, slide, diving board}\}$

Since, $n\left(A\right)=7$, then the number of all subsets of $A$ is $2^7=128$ subset.

Then,

The number of different variations of the pool which are possible is:

$\begin{gather*}{\color{#4257b2}128}\ \text{variations.}\end{gather*}$

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