Cardinality of Set of Subsets/Also presented as

Theorem

This result is also presented in the form:

The number of combinations of $n$ objects taken $m$ at a time

or:

The number of selections of $n$ objects taken $r$ at a time

or:

The number of ways of selecting $m$ objects out of $n$

or:

The number of ways of choosing $m$ objects from $n$ where order does not matter

or:

The number of ways of choosing a set of $m$ elements from the $n$ elements of the set $S$

Such wording is insufficiently precise for $\mathsf{Pr} \infty \mathsf{fWiki}$.

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text I$. Algebra: Permutations and Combinations
• 1964: A.M. Yaglom and I.M. Yaglom: Challenging Mathematical Problems With Elementary Solutions: Volume $\text { I }$ ... (previous) ... (next): Problems
• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.3$. Partitions: Example $35$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $35$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $35$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): selection