(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.