The number of proper subsets of the set ${1, 2, 3}$ is ___.

$8$

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$7$

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$6$

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$5$

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Solution

The correct option is B
$7$

A set of $n$ elements has $2^{n}$ subsets.
Every set is a subset of itself.
Thus, the number of proper subsets of a set is $2^{n} - 1$ subsets.
The set ${1, 2, 3}$ has 3 elements and hence, $2^{3} - 1 = 7$ proper subsets.

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