(3) There are two different ways to construct a permutation of k elements with j cycles:
Now take S to be the set of sequences of k elements selected from our n-element set without repetition.
The k smallest elements will be the first k elements.
The approach continues until we find k elements.
No algorithm is provided for selecting the greatest k elements since this should be done by inverting the ordering predicate.
We count the number of ways to choose k elements from an n-set.
Consider an algorithm to find the k element of an array.
As in selection sort, after k passes through the array, the first k elements are in sorted order.
The binomial coefficient can be interpreted as the number of ways to choose k elements from an n-element set.
There are ways to choose k elements from a set of n elements.
