# Number of Selections of 1 or More from Set/Examples/6

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## Example of Use of Number of Selections of $1$ or More from Set

Let there be $6$ different flowers in a vase.

Then there are $63$ different ways of selecting at least one of these flowers.

## Proof

Let $S$ be the set of flowers.

Let $N$ be the number of different ways of selecting at least one of these flowers.

We have:

- $\card S = 6$

where $\card S$ denotes the cardinality of $S$.

Hence from Number of Selections of $1$ or More from Set:

- $N = 2^6 - 1 = 63$

$\blacksquare$

## Sources

- 1953: L. Harwood Clarke:
*A Note Book in Pure Mathematics*... (previous) ... (next): $\text I$. Algebra: Permutations and Combinations: Exercises $\text I$: $9$