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Combinatorics: Number of subsets with cardinality k with 1 element.

A set n has elements $\{1,2,3,\dots,n\}$. How many subsets does it have of cardinality $k$ and that contains element $1$?

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marked as duplicate by Brian M. Scott, Mike Spivey, David Mitra, Thomas Andrews, Graphth Dec 11 '12 at 0:03

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Hint: After you put $1$ in each possible set, you then have to fill in the remaining $k-1$ spaces from the other $n-1$ elements. How many ways can you do this?

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